Coding and modulation apparatus using non-uniform constellation

ABSTRACT

A coding and modulation apparatus and method are presented. The apparatus ( 10 ) comprises an encoder ( 11 ) that encodes input data into cell words, and a modulator ( 12 ) that modulates said cell words into constellation values of a non-uniform constellation. The modulator ( 12 ) is configured to use, based on the total number M of constellation points of the constellation, the signal-to-noise ratio SNR in dB and the channel characteristics, a non-uniform constellation from a group of constellations comprising one or more of predetermined constellations defined by the constellation position vector u1 . . . v, wherein v=sqrt(M)/2−1.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of application Ser. No. 14/412,265, filed on Dec. 31, 2014, which is a National Stage Application of International Application No. PCT/EP2013/063824, filed on Jul. 1, 2013, which claims the benefit of priority from EP Application No. 13164169.8, filed Apr. 17, 2013 and EP Application No. 12175587.0, filed Jul. 9, 2012. The entire contents of each of the above applications are incorporated herein by reference in their entirety.

BACKGROUND

Field of the Disclosure

The present disclosure relates to a coding and modulation apparatus and method. Further, the present disclosure relates to a transmission apparatus and method. Still further, the present disclosure relates to a computer program and a non-transitory computer-readable recording medium.

Description of Related Art

Modern communications systems typically employ, among other elements, a coding and modulation apparatus (as part of a transmission apparatus) and a decoding and demodulation apparatus (as part of a receiving apparatus). The coding and modulation apparatus is often part of a so called BICM (Bit Interleaved Coded Modulation) apparatus, which generally comprises (at the transmitter side) a serial concatenation of a FEC (Forward Error Correction) encoder, a bit interleaver, and a modulator, which uses spectral efficient modulation such as multilevel PAM (Pulse Amplitude Modulation), PSK (Phase Shift Keying), or QAM (Quadrature Amplitude Modulation). It should be noted that hereinafter, whenever QAM is mentioned it should be understood as a generally term covering PAM, PSK and QAM.

BICM allows for good performance over both non-fading and fading channels due to the use of the interleaver and/or the FEC encoder. It has a reasonable decoding complexity as opposed to multilevel coding (MLC) coding schemes and is thus used frequently in communications systems, such as in all DVB systems, powerline communications (e.g., Homeplug AV, DAB, LTE, WiFi, etc.).

Generally, the coding and modulation capacity, such as the BICM capacity in systems using a BICM apparatus, is considered as a target function, and it is desired to find optimum constellation points such that this capacity is maximized, often subject to a power normalization, i.e., the average power of the constellation points should be normalized to e.g. 1.

The “background” description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventor(s), to the extent it is described in this background section, as well as aspects of the description which may not otherwise qualify as prior art at the time of filing, are neither expressly or impliedly admitted as prior art against the present disclosure.

SUMMARY

It is an object to provide a coding and modulation apparatus and method providing an increased or even maximized coding and modulation capacity. It is a further object to provide a demodulation and decoding apparatus and method as well as a corresponding computer program for implementing said methods and a non-transitory computer-readable recording medium for implementing said methods.

According to an aspect there is provided a coding and modulation apparatus comprising

-   -   an encoder that encodes input data into cell words, and     -   a modulator that modulates said cell words into constellation         values of a non-uniform constellation,         wherein said modulator is configured to use, based on the total         number M of constellation points of the constellation, the         signal-to-noise ratio SNR in dB and the channel characteristics,         a non-uniform constellation from a group of constellations         comprising one or more of the constellations defined by the         constellation position vector u_(1 . . . v), wherein         v=sqrt(M)/2−1, as described in detail in claim 1.

According to a further aspect there is provided a transmission apparatus comprising

-   -   a coding and modulation apparatus as proposed herein that         encodes and modulates input data into constellation values,     -   a converter that converts said constellation values into one or         more transmission streams to be transmitted, and     -   a transmitter that transmits said one or more transmission         streams.

According to still further aspects corresponding methods, a computer program comprising program means for causing a computer to carry out the steps of the coding and modulation method disclosed herein, when said computer program is carried out on a computer, as well as a non-transitory computer-readable recording medium that stores therein a computer program product, which, when executed by a processor, causes the coding and modulation method disclosed herein to be performed are provided.

Preferred embodiments are defined in the dependent claims. It shall be understood that the claimed methods, the claimed computer program and the claimed computer-readable recording medium have similar and/or identical preferred embodiments as the claimed apparatus and as defined in the dependent claims.

One of the aspects of the disclosure is that the constellation points of the used constellations are not located on a regular grid with equidistant symbols, but rather on optimized locations, dependent on the channel characteristics, e.g., channel transition probabilities due to AWGN (Additive White Gaussian Noise), fading, etc. Further, the used constellation is selected dependent on the SNR (signal-to-noise ratio) and the desired total number of constellation points of the used constellation. A method how to find and optimize these non-uniform constellations (in the following called NUCs) will be explained below.

It should be noted that to every M-QAM, one can also think of the underlying sqrt(M)-PAM. Further, it should be noted that in other aspects the group of constellations defined in the claims comprises less constellations, e.g. only constellations for non-fading channels, only constellations for fading channels, only constellations for selected values of M, only constellation for M-QAM or sqrt(M)-PAM and/or constellations for less SNR values. In other words, less constellations may be contained in the group of constellations available for use by the modulator, i.e. the group of constellations available for use by the modulator may comprise one or more of the constellations defined in the claims. Accordingly, the present disclosure is also directed to a coding and modulation apparatus and method that have a smaller group of constellations available for used and use (as explained above) and/or where less constellations are available for a particular value of M.

It should further be noted that for some values of M there are two options of constellations for fading channels and two options of constellations for non-fading channels provided for the same selection parameters (e.g. for the same SNR value) among which the modulation can select. These two options (referred to as 1. option and 2. option) are the result of separate optimizations of the coding and modulation capacity. Hence, for instance based on the desired capacity the modulator may select a constellation from the constellations according to the 1. option or the 2. option, wherein the constellations according to the 2. option generally provide a slightly higher capacity.

However, the constellation points of the QAM constellations considered in this disclosure are not located on a regular grid with equidistant symbols, but rather on optimized locations, dependent on the channel characteristics, e.g., channel transition probabilities due to AWGN, fading, etc.

It is to be understood that both the foregoing general description of the disclosure and the following detailed description are exemplary, but are not restrictive, of the disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the disclosure and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:

FIG. 1 shows an embodiment of a coding and modulation apparatus according to the present disclosure,

FIG. 2 shows an embodiment of a transmission apparatus according to the present disclosure,

FIG. 3 shows an embodiment of a communications system according to the present disclosure,

FIG. 4 shows a regular 4-QAM constellation as a simple example for a constellation,

FIG. 5A shows a diagram depicting an integrant of the 1-dimensional BICM capacity function at 30 dB SNR,

FIG. 5B shows a diagram depicting an integrant of the 1-dimensional BICM capacity function at 10 dB,

FIG. 6A shows a 8-PAM non-uniform constellation,

FIG. 6B shows a 64-QAM non-uniform constellation,

FIG. 7 shows a constellation for a 64-QAM non-uniform constellation generally defining the constellation points, and

FIG. 8 shows a diagram illustrating the performance of non-uniform N²-QAM constellations.

DESCRIPTION OF THE EMBODIMENTS

Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views, FIG. 1 shows an embodiment of a coding and modulation apparatus 10 according to the present disclosure. It comprises an encoder 11 that encodes input data into cell words, and a modulator 12 that modulates said cell words into constellation values of a non-uniform constellation. Said modulator 12 is configured to use (and, preferably, select in advance), based on the total number M of constellation points of the constellation, the signal-to-noise ratio SNR in dB and the channel characteristics, a non-uniform constellation from a group of constellations comprising predetermined constellations defined by the constellation position vector u_(1 . . . v), wherein v=sqrt(M)/2−1. These predetermined constellations will be derived and shown below.

In other embodiments of the coding and modulation apparatus 10 additional elements may be provided, such as a BCH encoder, an LCPC encoder, a bit interleaver and/or a demultiplexer (for demultiplexing bits of encoded data into the cell words). Some or all of these elements may separate elements or may be part of the encoder 11. For instance, a BICM device as conventionally used in the transmission apparatus of a DVB system may be used as coding and modulation apparatus 10.

FIG. 2 shows an embodiment of a transmission apparatus 20 according to the present disclosure comprising a coding and modulation apparatus 21 (referenced by 10 in FIG. 1) as proposed herein that encodes and modulates input data into constellation values, a converter 22 that converts said constellation values into one or more transmission streams to be transmitted, and a transmitter 23 that transmits said one or more transmission streams. In an exemplary embodiment the converter 22 may comprise one or more elements like a time, cell and/or frequency interleaver, a frame builder, an OFDM modulator, etc., as e.g. described in the various standards related to DVB. The constellations and the constellations values are generally predetermined and e.g. stored in a constellations storage 24 or retrieved from an external source.

In other embodiments of the transmission apparatus 20 addition elements may be provided, such as an input processing unit, a frame building unit and/or an OFDM generation unit as e.g. conventionally used in transmission apparatus of a DVB system.

FIG. 3 shows an embodiment of a communications system 30 according to the present disclosure comprising one (or more) transmission apparatus 20 (Tx) as shown in FIG. 2 and one or more receiving apparatus 40, 40′ (Rx).

A receiving apparatus 40 generally comprises a receiver 41 that receives one or more transmission streams, a deconverter 42 that deconverts the received one or more transmission streams into constellation values, and a demodulation and decoding apparatus 43 that demodulates and decodes said constellation values into output data. The demodulation and decoding apparatus 43 generally comprises a demodulator 44 for demodulating constellation values of a non-uniform constellation into cell words, and a decoder 45 for decoding cell words into output data words, wherein based on the total number M of constellation points of the constellation, the signal-to-noise ratio in dB and the channel characteristics, a non-uniform constellation is used from the group of constellations comprising the same predetermined constellations as used in the coding and modulation apparatus 10.

The preferred demodulation and decoding considers soft values as opposed to hard decided values (0 and 1). Soft values represent the continuously distributed received values (possibly after A/D conversion including quantization) by more than two states (as in the case of binary (hard) decision). The reason is that for hard decision, the NUCs are generally not optimal. Nowadays, BICM receivers typically are soft receivers anyway.

Generally, data (e.g. communications data, broadcast data, etc.) shall be transmitted from a transmission apparatus 20 to one or more of said receiving apparatus 40 over a transmission channel 50, 50′. The transmission channel 50, 50′ can be unicast channel, multicast channel, a broadcast channel and may be employed as one-directional or bi-directional channel (i.e. having a return channel from the receiving apparatus to the transmission apparatus).

In an embodiment the modulator 12 is configured to select and use a non-uniform constellation based on the total number M of constellation points of the constellation, the required signal-to-noise ratio SNR for error free decoding in dB and the channel characteristics. In broadcasting applications the constellation is generally not selected dependent on the SNR in the receiver, but dependent on the SNR that is required for error free decoding with a used channel code (if a code is used, for example LDPC codes in case of DVB 2^(nd) generation transmission systems) for an expected channel characteristic, e.g., static reception or multipath fading.

The total number M of constellation points is generally selected according to the desired payload throughput jointly with the code rate of the FEC encoder. The SNR for error free decoding for typical channel characteristic is generally known, e.g. by simulation. In broadcasting the channel characteristics of the receivers are not known, i.e. a compromise is selected. For instance, in broadcasting for each code rate of the FEC encoder one non-uniform constellation is selected, optimized for an SNR that is a compromise for all channel characteristics.

The transmitter generally targets a certain scenario. For instance, a broadcast transmission over cable or satellite considers the channel to be just a non-fading AWGN (appropriate channel model), while a terrestrial broadcaster typically considers the channel to be a fading channel, e.g. with Rayleigh distribution, as several echoes are usually received.

In another embodiment the modulator 12 is configured to adaptively select and use a non-uniform constellation based on the total number M of constellation points of the constellation, the signal-to-noise ratio SNR in dB and the channel characteristics, wherein said signal-to-noise ratio SNR in dB and channel characteristics are received from a receiving device 40 to which data shall be transmitted. Such an adaptive selection of the constellation is generally only possible with a return channel in unicast environments. A non-uniform constellation may be adapted e.g. in time and/or frequency domain, e.g. for different OFDM subcarriers.

Depending on the SNR the optimum value for M and the code rate of the FEC encoder can be selected, which offers the highest throughput (equivalent to C_(B)). In other words, for a large SNR a high value of M is selected leading to a high data throughput (and vice versa).

The channel characteristics describe the statistical properties of the channel, e.g., the extent of the multipath propagation of the transmission channel between transmitter and receiver. If the channel is characterized by no multipath propagation, corresponding to the AWGN channel, the required SNR for error free decoding is relatively low, i.e. the NUC has to be selected accordingly for optimum performance. If the transmission channel is characterized by strong multipath propagation, the required SNR for error free reception is larger compared to a channel without multipath propagation, i.e. a NUC optimized for higher SNR has to be used. Further, the NUCs should be optimized taking the fading characteristics into account, as will be discussed below.

As mentioned above, the number M of the constellation points of the constellations is selected according to the desired payload throughput. Larger values of M allow for higher data throughput, but require a larger SNR for error free reception. This is further influenced by the code rate of the FEC encoder, if any FEC encoder is used.

Another explanation (which is closely related to the optimization task of the present disclosure) is that for each SNR, optimized constellations are proposed for different M. The optimization target is the BICM capacity. For an expected SNR, say 15 dB of SNR should be guaranteed, M is chosen, for which the respective optimized NUC yields the largest BICM capacity. As a general rule it holds that for low SNR a low value of M should be selected and vice versa. But from a theoretical point of view, it turns out that high M is generally optimum, e.g., choosing M=4096 or M=1024 is preferred, because even for low SNR, the optimized NUC will “look (almost) like” a constellation with effectively smaller M, as several points will overlap. However, modulation and demodulation complexity increase with increasing M, so a tradeoff has to be considered.

As mentioned above known communications systems often employ among other blocks a so called BICM apparatus which may also be used as coding and modulation apparatus according to the present disclosure. The maximum possible capacity over a BICM apparatus is described by the BICM capacity C_(B):

$\begin{matrix} {{C_{B} = {{\sum\limits_{i = 0}^{m - 1}\; {E_{b,r_{k}}\;\left\lbrack {\log_{2}\frac{\sum\limits_{x_{l} \in _{b}^{i}}\; {p\left( {\left. r_{k} \middle| s_{k} \right. = x_{l}} \right)}}{p\left( r_{k} \right)}} \right\rbrack}} = {\int_{r_{k} \in {\mathbb{C}}}{\sum\limits_{i = 0}^{m - 1}\; {\sum\limits_{b = 0}^{1}\; {\sum\limits_{x_{l} \in _{b}^{i}}{{\frac{1}{M} \cdot {p\left( {\left. r_{k} \middle| s_{k} \right. = x_{l}} \right)}} \log_{2} \frac{\sum\limits_{x_{l} \in _{b}^{i}}\; {p\left( {\left. r_{k} \middle| s_{k} \right. = x_{l}} \right)}}{\frac{1}{M} \cdot {\sum\limits_{x_{l}^{\prime} \in }\; {p\left( {\left. r_{k} \middle| s_{k} \right. = x_{l}^{\prime}} \right)}}}{dr}_{k}}}}}}}},} & (1) \end{matrix}$

where I denotes the i-th bit label of the constellation point, and m is the total number of bits/QAM symbol point. Altogether the QAM constellation consists of M=2^(m) constellation points, each assigned a particular bit label (00 . . . 00, 00 . . . 01, . . . , 11 . . . 11). In (1), E[.] denotes expectation operator, p(r_(k)) is the probability density function (pdf) of the received symbols, s_(k) is the transmitted symbol according to a particular bit label, k is the discrete time (or subcarrier index in case of OFDM modulation), x₁ is a particular symbol of the set of all constellation symbols, this set being denoted by

(=symbol alphabet, with cardinality M=2^(m)).

p(r_(k)|s_(k)=x₁) is the likelihood function (transition probability—defined by the channel characteristics) that r_(k) is received given the fact that s_(k)=x₁ was transmitted. The subset

_(b) ^(i) includes all symbols from

, where the i-th bit label is b (either b=0 or b=1).

As seen in (1), C_(B) is a 2-dimensional integral. If only constellations are considered that can be split into two 1-dim. PAM constellations, it is easy to see that

C _(B)(2-dim.)=2×C _(B)(1-dim.)  (2)

All investigated channels here include AWGN (only or after the fading channel). This can be described by the signal-to-noise ratio SNR, typically in dB:

SNR=10*log₁₀(E _(s)/σ²),  (3)

where E_(s) is the average symbol power of the QAM constellation (typically normalized to 1), and σ² is the variance (=power) of the additive white Gaussian noise (which is assumed to be of zero-mean).

In (2), the 1-dimensional consideration for C_(B) (1-dim.) uses an N-PAM constellation, which has only half the symbol power, if just the projection on the in-phase or quadrature-phase, respectively, is taken. However, if again a power normalization to 1 is considered, the noise variance by a factor of 2 is increased. Thus, to be more precise, the target function for the optimization process considered according to the present disclosure is given by

C _(B)(2-dim. at SNRx)=2×C _(B)(1-dim. at SNRx/2),  (4)

where the 1-dimensional PAM has normalized power 1, thus just half the SNR (here, in absolute values, i.e. not in dB) as explained above. The 1-dimensional BICM capacity is also computed according to (1), where the 2-dimensional integral becomes a 1-dimensional integral with r_(k)ε

,

being the set of real numbers.

This equation (4) is optimized, given all degrees of freedom, namely the constellation points of the underlying 1-dim. constellation, subject to the power constraint, i.e.,

$\begin{matrix} {_{x} = {{E_{s_{k}}\left\lbrack {s_{k}}^{2} \right\rbrack} = {{E_{x_{l}}\left\lbrack {x_{l}}^{2} \right\rbrack} = {{\frac{1}{M}{\sum\limits_{l = 0}^{M - 1}\; {x_{l}}^{2}}}\overset{!}{=}1}}}} & (5) \end{matrix}$

For example, a regular 4-QAM consists of constellation points (e^(jπ/4), e^(j7π/4), e^(3π/4), e^(j5π/4)), as can be seen in FIG. 4. The average symbol power is 1 (all symbols are located on unit circle here). The above symbol vector (e^(jπ/4), e^(j7π/4), e^(3π/4), e^(j5π/4)) is to be understood such that the first entry (e^(jπ/4)) belongs to the bit vector 00, the second entry (e^(j7π/4)) to 01 and so on, i.e. the entries belong to bit vectors with increasing values, where the first bit position is the most significant bit (MSB) and the last one the least significant bit (LSB). This 4-QAM is a particular case of an N²-QAM, with N=2. Note that this definition (of being an N² QAM) does not only require N² being a square number (N²=2²), but also that the constellation is symmetrical and can be described by two independent N-PAM constellations, here a 2-PAM: the in-phase component (real-part of the complex symbols) is a 2-PAM with symbol vector (1/sqrt(2), −1/sqrt(2)) and describes the 1^(st) bit of the 4-QAM, whereas the quadrature-phase component (imaginary-part of the complex symbols) is the same 2-PAM, this time describing the 2^(nd) bit of the 4-QAM. Note further that the decomposition of the N²-QAM into two N-PAMs is only possible if the bit labeling is according to binary reflected Gray mapping, which is typically applied (e.g. in DVB-systems).

The above example can be extended to higher order N²-QAMs, with M>2. Then the underlying N-PAM describes for one component the 1^(st), 3^(rd), 5^(th) and so on bit label, while for the other component it describes the 2^(nd), 4^(th), 6^(th) and so on label.

Constellation shaping is generally known and has a long history. Only in recent years, constellations were investigated which maximize the BICM capacity C_(B). In [6], the authors propose an heuristic approach to maximize C_(B) by forcing the underlying PAM to approach a Gauss-like form (as is well known from Shannon's capacity theorem, the optimum constellation over the AWGN channel should have a Gaussian distribution; note that this means that there is an infinite number of continuously distributed input signals, having a Gaussian distribution, i.e., symbols with small power should occur more frequently than symbols with large power). There is no proof that this maximizes C_(B), indeed those NUCs designed according to this method do not maximize C_(B). The resulting NUCs are in general no N² NUCs, i.e., a 2-dimensional NUC was optimized, not the underlying PAM. However, in N. Muhammad, “Coding and modulation for spectral efficient transmission”, Ph.D. dissertation, Universität Stuttgart, Institut für Nachrichtenübertragung, Pfaffenwaldring 47, 70569 Stuttgart, Germany, June 2006, the first time constellations have been directly optimized with respect to the target function C_(B). For this method two differences to the current method occur:

-   -   M-NUCs were proposed for M=8, 16, and 32. No higher order NUCs         were investigated, as the optimization becomes very time         consuming and the optimization algorithms became numerically         unstable.     -   The optimization algorithm was a hand-written gradient search         algorithm, where both the BICM capacity and the gradient thereof         consisted of improper integrals. No special care about either         the numerical solution of the improper integral or the         problematic integrants was considered. This consideration of         these two issues is fundamental to obtain results for high order         constellations, such as 1 k (i.e. 1024) NUC.

As described above, two problems arise when solving the optimization:

a) improper integral: integration border selection; and b) integrant.

With respect to problem a) (improper integral: integration border selection), as seen in eq. (1), the BICM capacity involves an integral from −infinity to +infinity (=improper integral). Any numerical solution of this integral has to consider finite integration borders such as from −b to +b, with b sufficiently large. Matlab provides several functions for numerical integration, even for improper integrals, such as the function “quad”, which internally optimizes the appropriate integration borders b. However, it has been observed that even these functions yield numerical instabilities and do not end up with the correct integral.

It can be observed that the integrant in (1) approaches 0 if the variable r_(k) is sufficiently large (b→lnf). So a naïve approach would be to stepwise increase the variable r_(k), until the integrant falls below a certain threshold (say 10⁻³⁰⁰ or if it even becomes exactly 0) and chose this value for the integration border b.

However, it has further been observed that the integrant can take on very small values even before it converges to 0 for large variables, as can be seen in the two examples depicted in FIGS. 5A and 5B: the plot shown in FIG. 5B is the integrant of the 1-dimensional BICM capacity function, if a regular 32-PAM is used, at 10 dB SNR, while the plot shown in FIG. 5A 30 dB is considered.

Note that for 30 dB, many very small integrant values occur in the interval [−2,2] and any optimized integration border would be misleading in this interval. Thus, it is proposed to find the optimum (=numerically correct) integration border b as follows:

i) start with a large positive value S, iteratively reduce the value by decrements D, compute the integrant with this value as variable r_(k), until the first non-zero value of the integrant is computed. If no non-zero integrant can be found before r_(k)=0, start again with a larger initial value S (say 10 times larger than before) and reduce D (say by factor of 10) to have a larger search interval and a finer granularity. ii) As this search is time consuming, it is proposed to adjust the initial value S and the decrement D according to the SNR. If σ² is the noise variance of the 1-dimensional mapping (see eq. (3)), then as a good compromise S=4000*σ² and D=50*σ² has been chosen.

With respect to problem b) (integrant) it has further been observed that the integrant of the BICM capacity integral can cause numerical instabilities for large SNR values. As can be seen in eq. (1), the integrant consists of sums, including terms such as

x*log(x),x*log(1/x), or x*1/log(x).

The value of x is e.g. the transition probability p(r_(k)|s_k=x₁), or a pdf or includes parts thereof. The values of x become increasingly small (even approaching 0) if the SNR is very large, as the pdfs typically correspond to Gaussian distributions. Thus, the following limits might occur:

lim_({x) _(→) _(0}) x*log(x),lim_({x) _(→) _(0}) x*log(1/x), or lim_({x) _(→) ₀ }x*1/log(x).

Note that in theory, each limit converges to 0 (see l'Hospital's rule), but in a numerical computation, values such as + or − infinite or NaN (“not a number”) will occur. Thus, the following is proposed: during the computation of each element (i.e., each addend in the integrant of (1)), the value has to be checked if it is finite (otherwise infinite or NaN), and replace it by 0 in case it is not finite. Only this way, reliable integration results can be obtained.

With the above considerations, N²-NUCs have been optimized as one embodiment with N² being 16, 64, 256, 1024 (1 k), 4 k, 16 k, 64 k, 256 k and 1024 k. This means, the target function C_(B) of the underlying 1-dimensional PAM is used and the degrees of freedom (the real-valued constellation points of the PAM) are optimized. Note that the PAM has only N=sqrt(N²) degrees of freedom (e.g. a 64-NUC is based on an 8-PAM). Due to symmetry, the negative constellation values are the same as their positive counterparts, such that only N/2 degrees of freedom remain. Finally, one more degree of freedom is lost due to the power normalization (5). The 64-NUC can thus be optimized by considering only 3 degrees of freedom (“dof”, i.e., optimization variables).

The presented optimization is preferably based on the Matlab's fmincon function for constrained nonlinear optimization: the target function is the BTCM capacity, the constraints are as follows:

-   -   all dof (degrees of freedom) >0;     -   all dof need to fulfill the power normalization, when the N-PAM         is created based on them;     -   the dof must occur in increasing order.

The function fmincon requires an initial set of dof, where the values were taken from a regular, i.e. uniform constellation, but a random mutation was applied on them. It is to be noted that the resulting values should still be in increasing order, otherwise the Gray bit labeling is not fulfilled anymore. The NUCs will be described by their degrees of freedom, e.g., a 64-NUC optimized for the AWGN channel at SNR=11.5 dB yields the following values (optimized degrees of freedom):

-   -   2.2794 4.6229 7.5291.         This means that the positive constellation values are     -   1 2.2794 4.6229 7.5291         (the 1 was redundant, due to the power normalization, which will         be applied in the end). The underlying 1-dim. 8-PAM NUC is thus         described by the symbol vector     -   (1.6405 1.0073 0.2179 0.4967 −1.6405 −1.0073 −0.2179 −0.4967),         where the values are already normalized to unit average power.

As described before, the first entry (1.6405) corresponds to the bit label 000, the next one (1.0073) to 001 and so on. The 2-dim. 64-NUC is then obtained by symmetry, where both in-phase and quadrature-phase component of the NUC are based on the 8-PAM NUC.

FIG. 6A shows a 8-PAM NUC while FIG. 6B shows a 64-QAM NUC. The bit labels are given in integer numbers (000→0, 001→1, 010→2 and so on).

The creation of the 2-dim. NUC based on the optimized degrees of freedom will be explained in more detail below.

Since the performance of NUCs depends on the SNR value they are optimized for, a thorough selection is preferably carried out depending on the (FEC) code rate to achieve optimum performance. If the channel characteristics are known, the required SNR value for FEC convergence can be determined by simulation. Then the NUC that has been optimized for this SNR value is chosen for best performance. If the SNR at the receiver is lower than this SNR decoding threshold, the constellation is not optimal. However, this is no drawback, since the BICM capacity is too low for successful decoding anyhow. On the other hand if the SNR at the receiver is clearly higher than the decoding threshold, a sufficient amount of BICM capacity for successful decoding is available, even though the NUC is suboptimal for this SNR range. Therefore, the NUC needs to be optimized for the SNR value at the waterfall region (i.e., decoding threshold for (quasi-) error free decoding) of the FEC. As the SNR value of the waterfall region depends on the code rate of the FEC, a different NUC is selected for each code rate.

The SNR value for (quasi-) error free decoding also depends on the channel characteristics of the receiver. For instance the required SNR for error free decoding of the DVB-T2 LDPC code in the AWGN channel is 0.8 dB, whereas 2.5 dB are required in the Rayleigh P1 multipath channel. The selected NUC for each code rate is thus not optimal in all channel environments and a tradeoff is necessary in a broadcasting environment that suits all (or most) users in the network. In a point-to-point network with return channel, the optimal NUC may be selected based on the measured channel characteristics in the receiver.

Currently, there exist no optimized constellations for fading channels. If the transmitter has no channel state information (CSI), but the receiver has perfect CSI (due to, e.g., pilot-based channel estimation), then the average BICM is the target function, which needs to be optimized for NUCs designed for fading channels. If the magnitude of the fading value for one QAM symbol is denoted as h (e.g. for a particular time instant and/or a particular subcarrier in case of OFDM), then the instantaneous BICM capacity is called C_(B)(h) and given acc. to eq. (1). Note that the pdfs and transition probabilities in (1) are now different from the pure AWGN channel. E.g. in the AWGN case, the likelihood function p(r_(k)|s_(k)=x₁) was given by a Gaussian distribution with zero-mean and variance σ². Now, for fading with the value h, the distribution is still Gaussian with zero-mean, but with instantaneous variance σ²/h².

A good model for the fading statistics is given by a Rayleigh distribution of the fading magnitude h. Thus, the pdf of h is:

p(h)=h/σ _(h) ²*exp(−h ²/(2*σ_(h) ²)),  (6)

where σ_(h) ² is the variance of the Rayleigh distribution. For a passive channel, i.e. one which on average neither attenuates nor magnifies the signal, σ_(h) ²=½. This means, that the average SNR over a fading channel is the same as of a non-fading channel.

Now, the average BICM capacity over many channel realizations is given by

C _(B)=∫₀ ²⁸ p(h)*Cb(h)dh,  (7)

i.e., the instantaneous BICM capacity as a function of h has to be multiplied by the pdf of h (see (6)) and integrated over all possible fading magnitudes (0 . . . infinity).

Again, an improper integral has to be solved. This time, the integrant of (7) converges to 0 due to the pdf of h. It was found that a sufficiently large upper limit for the integral in (7) is given by 38, independent of the instantaneous capacity C_(B)(h). This enables faster optimization of (7). Results will be shown below for N²-NUCs, N²=16, 64, 256, 1024 (1 k), 4096 (4 k) and 16384 (16 k).

The same principle regarding the selection of the NUC that has been described for static channels also holds for receivers experiencing fading channels, e.g., portable or mobile receivers. But since in fading channels the SNR in the receiver is varying due to the fading effect of the channel, the NUC cannot always operate at the optimum SNR. In general, the NUCs optimized for the fading channel perform better compared to the NUCs optimized for the non-fading channel when used at SNR values for which they are initially not optimized for, i.e. they perform better over broader SNR regions. Moreover, it was found that the NUCs optimized for the Rayleigh fading channel are good for most fading channels, e.g., with Rice distribution, with more than one echo component (e.g. TU6 channel) or with time- and frequency-selective fading with correlation. This is because the optimization considers the average of several channel instances/realizations.

In the following some more explanation is provided regarding the definition of the non-uniform QAM constellations. Each input cell word (y_(0,q) . . . y_(m-1,q)) (i.e. provided to the modulator) shall be modulated using a non-uniform QAM constellation to give a constellation point z_(q) prior to normalization, where m corresponds to the number of bits per QAM symbol m=log₂(M). It should be noted that the parameter q used here for discrete time or subcarrier index corresponds to the parameter k as used in the above. The exact values of the real and imaginary components Re(z_(q)) and Im(z_(q)) for each combination of the relevant input bits y_(0 . . . m-1,q) are given in the following tables for the various constellation sizes depending on the NUC position vector u_(1 . . . v), which defines the constellation point position of the non-uniform constellation. The length of the NUC position vector u is defined by

$v = {\frac{\sqrt{M}}{2} - 1.}$

In one example, the corresponding constellation point z_(q) for a 64-QAM NUC defined by the NUC position vector (u_(1 . . . 3))=(2,5,6) and the input cell word (y_(0,q) . . . y_(m-1,q)=(100111) is Re(z_(q))=−u₂=−5 and Im(z_(q))=u₁=2. The complete constellation for this NUC position vector is shown in FIG. 7 with exemplary input cell words marked at the corresponding constellation points.

The resulting constellation mapping (also called labeling) for the non-uniform constellations follows a binary reflected Gray-Mapping (labeling), i.e. neighboring constellation points differ in only one bit. The power of the constellation points z_(q) is normalized such that the expectation value of the normalized constellation point f_(q) equals 1, i.e. E(|f_(q)|²)=1. For example, the normalized constellation value f_(q) of a uniform 16-QAM constellation results by

$f_{q} = {\frac{z_{q}}{\sqrt{10}}.}$

FIG. 8 shows a diagram illustrating the performance of non-uniform N²-QAM constellations.

The following tables define the constellation position vectors (prior to power normalization) as well as the bit labelling of the data cell words to the constellation points.

Constellation Mapping for Real Part of 16-QAM

y_(0,q) 1 1 0 0 y_(2,q) 0 1 1 0 Re(z_(q)) −3 −1 1 3 Uniform −u₁ −1 1 u₁ NUC

Constellation Mapping for Imaginary Part of 16-QAM

y_(1, q) 1 1 0 0 y_(3, q) 0 1 1 0 Im(z_(q)) −3 −1 1 3 Uniform −u₁ −1 1 u₁ NUC

Constellation Mapping for Real Part of 64-QAM

y_(0, q) 1 1 1 1 0 0 0 0 y_(2, q) 0 0 1 1 1 1 0 0 y_(4, q) 0 1 1 0 0 1 1 0 Re(z_(q)) −7 −5 −3 −1 1 3 5 7 Uniform −u₃ −u₂ −u₁ −1 1 u₁ u₂ u₃ NUC

Constellation Mapping for Imaginary Part of 64-QAM

y_(1, q) 1 1 1 1 0 0 0 0 y_(3, q) 0 0 1 1 1 1 0 0 y_(5, q) 0 1 1 0 0 1 1 0 Im(z_(q)) −7 −5 −3 −1 1 3 5 7 Uniform −u₃ −u₂ −u₁ −1 1 u₁ u₂ u₃ NUC

Constellation Mapping for Real Part of 256-QAM

y_(0, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(2, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(4, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(6, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) −15 −13 −11 −9 −7 −5 −3 −1 1 3 5 7 9 11  13  15  Uniform −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 1 u₁ u₂ u₃ u₄ u₅ u₆ u₇ NUC

Constellation Mapping for Real Part of 256-QAM

y_(1, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(3, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(5, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(7, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) −15 −13 −11 −9 −7 −5 −3 −1 1 3 5 7 9 11  13  15  Uniform −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 1 u₁ u₂ u₃ u₄ u₅ u₆ u₇ NUC

Constellation Mapping for Real Part of 1024-QAM

Y_(0, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(2, q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(4, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(6, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(8, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) −31  −29 −27 −25 −23 −21 −19 −17 −15 −13 −11 −9 −7 −5 −3 −1 Uniform −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉ −u₈ −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 NUC Y_(0, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(2, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(4, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(6, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(8, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Uniform 1  u₁  u₂  u₃  u₄  u₅  u₆  u₇  u₈  u₉  u₁₀  u₁₁  u₁₂  u₁₃  u₁₄ u₁₅ NUC

Constellation Mapping for Imaginary Part of 1024-QAM

y_(1, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(3, q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(5, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(7, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(9, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) −31  −29 −27 −25 −23 −21 −19 −17 −15 −13 −11 −9 −7 −5 −3 −1 Uniform −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉ −u₈ −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 NUC y_(1, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(3, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(5, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(7, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(9, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Uniform 1  u₁  u₂  u₃  u₄  u₅  u₆  u₇  u₈  u₉  u₁₀  u₁₁  u₁₂  u₁₃  u₁₄ u₁₅ NUC

Constellation Mapping for Real Part of 4096-QAM

Y_(0, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(2, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(4, q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(6, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(8, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(10, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) −63 −61 −59 −57 −55 −53 −51 −49 −47 −45 −43 −41 −39 −37 −35 −33 Uniform −u₃₁ −u₃₀ −u₂₉ −u₂₈ −u₂₇ −u₂₆ −u₂₅ −u₂₄ −u₂₃ −u₂₂ −u₂₁  −u₂₀  −u₁₉  −u₁₈  −u₁₇  −u₁₆  NUC Y_(0, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(2, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(4, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(6, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(8, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(10, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) −31 −29 −27 −25 −23 −21 −19 −17 −15 −13 −11 −9 −7 −5 −3 −1 Uniform −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉   −u₈   −u₇   −u₆   −u₅  −u₄  −u₃  −u₂  −u₁  −1 NUC Y_(0, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(2, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(4, q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(6, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(8, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(10, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Uniform 1  u₁  u₂  u₃  u₄  u₅  u₆  u₇  u₈  u₉ u₁₀ u₁₁ u₁₂ u₁₃ u₁₄ u₁₅ NUC Y_(0, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(2, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(4, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(6, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(8, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(10, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 Uniform  u₁₆  u₁₇  u₁₈  u₁₉  u₂₀  u₂₁  u₂₂  u₂₃  u₂₄  u₂₅ u₂₆ u₂₇ u₂₈ u₂₉ u₃₀ u₃₁ NUC

Constellation Mapping for Imaginary Part of 4096-QAM

y_(1, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(3, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(5, q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(7, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(9, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(11, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) −63 −61 −59 −57 −55 −53 −51 −49 −47 −45 −43 −41 −39 −37 −35 −33 Uniform −u₃₁ −u₃₀ −u₂₉ −u₂₈ −u₂₇ −u₂₆ −u₂₅ −u₂₄ −u₂₃ −u₂₂ −u₂₁  −u₂₀  −u₁₉  −u₁₈  −u₁₇  −u₁₆  NUC y_(1, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(3, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(5, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(7, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(9, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(11, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) −31 −29 −27 −25 −23 −21 −19 −17 −15 −13 −11 −9 −7 −5 −3 −1 Uniform −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉  −u₈  −u₇  −u₆  −u₅  −u₄  −u₃  −u₂  −u₁  −1 NUC y_(1, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(3, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(5, q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(7, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(9, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(11, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Uniform 1  u₁  u₂  u₃  u₄  u₅  u₆  u₇  u₈  u₉ u₁₀ u₁₁ u₁₂ u₁₃ u₁₄ u₁₅ NUC y_(1, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(3, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(5, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(7, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(9, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(11, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 Uniform  u₁₆  u₁₇  u₁₈  u₁₉  u₂₀  u₂₁  u₂₂  u₂₃  u₂₄  u₂₅ u₂₆ u₂₇ u₂₈ u₂₉ u₃₀ u₃₁ NUC

In the following the definition of the NUC position vectors obtained by use of the above described approach is provided. The signal-to-noise ratio (SNR) is always denoted in dB and corresponds to the average SNR in case of fading channels.

a1) 16-QAM or 4-PAM for a Non-Fading Channel (1. Option)

SNR 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 u₁ 1.0001 1.0001 1.0002 1.1550 1.6201 1.9580 2.2633 2.5594 2.8411 3.0980 3.3357 3.5294 3.6712 3.7520 SNR 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 u₁ 3.7812 3.7480 3.6736 3.5998 3.5184 3.4446 3.3818 3.3239 3.2786 3.2407 3.2109 3.1793 3.1581 3.1390 SNR 14 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 u₁ 3.1219 3.1078 3.0964 3.0819 3.0774 3.0665 3.0579 3.0528 3.0485 3.0423 3.0411 3.0333 3.0521

a2) 16-QAM or 4-PAM for a Fading Channel (1. Option)

SNR 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 u₁ 1.6289 1.8484 2.0415 2.2247 2.3853 2.5335 2.6736 2.7962 2.8980 2.9832 3.0593 3.1169 3.1616 3.1973 SNR 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 u₁ 3.2180 3.2334 3.2427 3.2473 3.2477 3.2463 3.2436 3.2388 3.2312 3.2291 3.2224 3.2149 3.2129 3.2055 SNR 14 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 u₁ 3.2036 3.1976 3.1953 3.1917 3.1854 3.1853 3.1803 3.1799 3.1761 3.1712 3.1715 3.1721 3.1711

a3) 16-QAM/4-PAM for a Non-Fading Channel (2. Option)

SNR/u 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 u₁ 1.0001 1.0001 1.0002 1.155 1.6201 1.958 2.2633 2.5594 2.8411 3.098 3.3357 3.5294 3.6712 3.752 SNR/u 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 u₁ 3.7812 3.748 3.6736 3.5998 3.5184 3.4446 3.3818 3.3239 3.2786 3.2407 3.2109 3.1793 3.1581 3.139 SNR/u 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 u₁ 3.1219 3.1078 3.0964 3.0819 3.0774 3.0665 3.0579 3.0528 3.0485 3.0423 3.0411 3.0333 3.0521

a4) 16-QAM/4-PAM for a Fading Channel (2. Option)

SNR 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 u₁ 1.6289 1.8484 2.0415 2.2247 2.3853 2.5335 2.6736 2.7962 2.898 2.9832 3.0593 3.1169 3.1616 3.1973 SNR 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 u₁ 3.218 3.2334 3.2427 3.2473 3.2477 3.2463 3.2436 3.2388 3.2312 3.2291 3.2224 3.2149 3.2129 3.2055 SNR 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 u₁ 3.2036 3.1976 3.1953 3.1917 3.1854 3.1853 3.1803 3.1799 3.1761 3.1712 3.1715 3.1721 3.1711

b1) 64-QAM or 8-PAM for a Non-Fading Channel (1. Option)

SNR 5 6 7 8 9 10 11 12 13 14 15 16 17 u₁ 1.0000 1.0022 1.0009 1.1945 1.4265 1.7169 2.0784 2.4886 2.8098 2.9798 3.0657 3.0895 3.0744 u₂ 2.6799 3.6839 3.7714 3.5638 3.6893 3.9984 4.4060 4.8482 5.2018 5.4093 5.5100 5.4881 5.3864 u₃ 3.4087 3.6839 3.7779 4.6322 5.4024 6.2400 7.1114 7.9262 8.4762 8.7005 8.7024 8.4935 8.1750 SNR 18 19 20 21 22 23 24 25 26 27 28 29 30 u₁ 3.0557 3.0409 3.0309 3.0244 3.0180 3.0140 3.0153 3.0107 3.0001 2.7744 2.2837 3.0137 1.9278 u₂ 5.2889 5.2157 5.1647 5.1260 5.0979 5.0766 5.0685 5.0403 5.0254 4.5265 3.3188 5.1307 3.2632 u₃ 7.8949 7.6816 7.5265 7.4114 7.3213 7.2517 7.2083 7.1286 7.1277 6.6760 5.0386 6.6178 4.4151

b2) 64-QAM or 8-PAM for a Fading Channel (1. Option)

SNR 5 6 7 8 9 10 11 12 13 14 15 16 17 u₁ 1.0353 1.1062 1.2092 1.3451 1.5409 1.8112 2.1208 2.3945 2.6067 2.7560 2.8505 2.9120 2.9496 u₂ 2.8206 2.9015 3.0799 3.2980 3.5826 3.9386 4.3237 4.6577 4.9074 5.0773 5.1674 5.2201 5.2393 u₃ 3.4534 3.9220 4.4154 4.9297 5.5069 6.1594 6.8108 7.3475 7.7177 7.9488 8.0398 8.0680 8.0538 SNR 18 19 20 21 22 23 24 25 26 27 28 29 30 u₁ 2.9751 2.9907 3.0032 3.0055 3.0126 3.0124 3.0136 3.0165 3.0156 3.0158 3.0160 3.0180 3.0183 u₂ 5.2491 5.2493 5.2489 5.2365 5.2375 5.2247 5.2182 5.2165 5.2098 5.2070 5.2040 5.2036 5.1995 u₃ 8.0217 7.9849 7.9528 7.9035 7.8862 7.8443 7.8194 7.8046 7.7839 7.7661 7.7620 7.7569 7.7566

b3) 64-QAM/8-PAM for a Non-Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 1.0007 1.0017 0.7353 0.9997 1.0002 0.9998 1.0001 1 1.1927 1.4264 1.7169 2.0738 2.4886 2.8112 u2 1.0005 1.0004 1.0005 2.2657 2.8429 3.337 3.6717 3.7738 3.5613 3.6905 3.9984 4.3992 4.8482 5.2041 u3 0.9998 0.9999 1.4855 2.2642 2.842 3.3367 3.6718 3.775 4.6253 5.4009 6.24 7.1031 7.9262 8.4801 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 2.9803 3.0658 3.089 3.0745 3.0551 3.0408 3.0308 3.0234 3.0183 3.0146 3.0117 3.006 2.9999 3.0181 u2 5.4101 5.5099 5.4876 5.3868 5.288 5.2157 5.1639 5.1262 5.0982 5.0776 5.0613 5.0467 5.0116 5.0174 u3 8.7018 8.7025 8.4931 8.1754 7.8925 7.6814 7.5255 7.4093 7.3204 7.2536 7.2029 7.156 7.1015 7.12 SNR 28 29 30 u1 3.1429 2.5878 2.6804 u2 5.2147 4.0051 4.2638 u3 7.481 5.6207 5.7796

b4) 64-QAM/8-PAM for a Fading Channel (2. Option)

SNR 5 6 7 8 9 10 11 12 13 14 15 16 17 18 u1 1.0353 1.1062 1.2092 1.3451 1.5409 1.8112 2.1208 2.3945 2.6067 2.756 2.8505 2.912 2.9496 2.9751 u2 2.8206 2.9015 3.0799 3.298 3.5826 3.9386 4.3237 4.6577 4.9074 5.0773 5.1674 5.2201 5.2393 5.2491 u3 3.4534 3.922 4.4154 4.9297 5.5069 6.1594 6.8108 7.3475 7.7177 7.9488 8.0398 8.068 8.0538 8.0217 SNR 19 20 21 22 23 24 25 26 27 28 29 30 u1 2.9907 3.0032 3.0055 3.0126 3.0124 3.0136 3.0165 3.0156 3.0158 3.016 3.018 3.0183 u2 5.2493 5.2489 5.2365 5.2375 5.2247 5.2182 5.2165 5.2098 5.207 5.204 5.2036 5.1995 u3 7.9849 7.9528 7.9035 7.8862 7.8443 7.8194 7.8046 7.7839 7.7661 7.762 7.7569 7.7566

c1) 256-QAM or 16-PAM for a Non-Fading Channel (1. Option)

SNR 5 6 7 8 9 10 11 12 13 14 15 16 17 u₁ 1.0097 1.0665 1.0768 1.0930 1.1066 1.0503 1.0278 1.0000 1.0000 1.0000 1.0000 1.0256 1.1132 u₂ 1.0243 1.4150 1.2578 1.4817 1.7257 1.9773 2.1334 2.3571 2.6866 2.8218 2.9484 3.0100 3.0828 u₃ 1.0300 1.6034 1.2587 1.5300 1.7257 1.9773 2.1334 2.3622 2.7092 2.8892 3.1149 3.2249 3.4673 u₄ 2.6821 3.3596 3.4255 3.7766 3.9138 4.1612 4.3125 4.4722 4.8316 4.9033 5.1366 5.2497 5.4373 u₅ 2.6821 3.3596 3.4255 3.7766 3.9375 4.1734 4.4861 4.8450 5.3535 5.5528 5.8510 6.0534 6.5183 u₆ 3.3063 4.0879 4.3286 4.6970 5.0898 5.6363 6.3912 6.8392 7.6085 7.9200 8.3122 8.4791 8.8521 u₇ 3.6820 4.7573 4.7284 5.4489 6.2380 6.5675 7.7493 8.8112 10.0024 10.6021 11.1960 11.3836 11.7747 SNR 18 19 20 21 22 23 24 25 26 27 28 29 30 u₁ 1.3440 2.0909 2.7505 2.9606 3.0120 3.0176 3.0142 3.0104 3.0073 3.0054 3.0042 3.0022 2.9919 u₂ 3.2921 4.0957 4.8095 5.0402 5.0981 5.0934 5.0719 5.0525 5.0386 5.0269 5.0222 5.0150 5.0017 u₃ 4.0379 5.5745 6.8101 7.2061 7.2981 7.2676 7.2042 7.1500 7.1120 7.0845 7.0663 7.0475 7.0199 u₄ 5.9945 7.7068 9.1334 9.6065 9.6891 9.5883 9.4460 9.3305 9.2485 9.1897 9.1488 9.1103 9.0581 u₅ 7.5727 9.9098 11.7487 12.3192 12.3427 12.1129 11.8445 11.6314 11.4793 11.3645 11.2861 11.2158 11.1448 u₆ 9.9517 12.7455 14.9217 15.4925 15.3646 14.9269 14.4704 14.1111 13.8500 13.6527 13.5110 13.3957 13.2816 u₇ 13.0332 16.3954 18.9099 19.3657 18.9656 18.2095 17.4738 16.8947 16.4666 16.1368 15.8975 15.6946 15.5305

c2) 256-QAM or 16-PAM for a Fading Channel (1. Option)

SNR 5 6 7 8 9 10 11 12 13 14 15 16 17 u₁ 1.0356 1.0100 1.0290 1.0219 1.0329 1.0094 1.0111 1.0000 1.0000 1.0001 1.0246 1.1185 1.3950 u₂ 1.3828 1.3870 1.5299 1.4838 1.7668 1.9127 2.1472 2.2908 2.4733 2.6105 2.7092 2.8453 3.1765 u₃ 1.3992 1.3870 1.5492 1.4838 1.7668 1.9127 2.1472 2.3051 2.5255 2.7354 2.9390 3.2706 3.9636 u₄ 3.0045 3.1253 3.3047 3.3824 3.7309 3.9074 4.1429 4.3242 4.5173 4.6739 4.8281 5.1438 5.9227 u₅ 3.0045 3.1449 3.3048 3.4113 3.7801 4.0235 4.3590 4.7401 5.0524 5.3659 5.7359 6.3140 7.4309 u₆ 3.6491 4.1004 4.3581 4.6594 5.1755 5.6876 6.0417 6.6189 7.0304 7.3939 7.7768 8.4290 9.7743 u₇ 4.3373 4.5258 4.9468 5.3793 5.9000 6.6271 7.4630 8.7179 9.2916 9.7803 10.2831 11.1015 12.7817 SNR 18 19 20 21 22 23 24 25 26 27 28 29 30 u₁ 1.8520 2.2282 2.4888 2.6609 2.7728 2.8431 2.8888 2.9170 2.9375 2.9504 2.9593 2.9671 2.9692 u₂ 3.7148 4.1544 4.4597 4.6629 4.7937 4.8730 4.9250 4.9552 4.9771 4.9892 4.9973 5.0074 5.0060 u₃ 4.9210 5.6758 6.1947 6.5358 6.7533 6.8809 6.9632 7.0090 7.0410 7.0554 7.0668 7.0806 7.0767 u₄ 7.0428 7.9073 8.4842 8.8475 9.0687 9.1840 9.2515 9.2802 9.2999 9.2969 9.2999 9.3060 9.2919 u₅ 8.9081 10.0295 10.7658 11.2198 11.4828 11.6084 11.6720 11.6871 11.6912 11.6733 11.6622 11.6610 11.6332 u₆ 11.5661 12.8870 13.7176 14.1966 14.4408 14.5284 14.5407 14.5072 14.4683 14.4127 14.3708 14.3439 14.2915 u₇ 14.9910 16.5637 17.4984 17.9831 18.1769 18.1849 18.1070 17.9950 17.8844 17.7634 17.6707 17.6011 17.5056

c3) 256-QAM/16-PAM for a Non-Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9987 1 0.8555 0.9986 1.0007 0.9999 1 1.0001 1.1538 1.2053 1.1098 1.0113 0.9755 0.961 u2 0.9995 0.9988 0.6438 0.999 1.0022 1.0008 0.9997 1 1.3318 1.4592 1.5806 1.8511 2.1909 2.5454 u3 1.0006 1.0012 0.7241 0.9997 1.0003 0.9994 1.0002 1 1.1537 1.2044 1.4081 1.7918 2.1934 2.5919 u4 1.0014 0.9977 0.9802 2.2701 2.8454 3.336 3.6707 3.7727 4.0051 4.1314 3.8919 3.9933 4.2942 4.6269 u5 0.9994 0.9966 0.8403 2.261 2.8447 3.3359 3.6718 3.7726 3.5919 3.7449 3.8725 4.2278 4.6785 5.1556 u6 0.9984 0.9972 1.2098 2.2574 2.8455 3.3381 3.6727 3.7737 4.0063 4.1297 4.7175 5.7442 6.5854 7.3386 u7 1.0001 0.9996 1.4732 2.265 2.8465 3.3369 3.6713 3.7738 5.9093 6.4423 6.812 7.6428 8.6591 9.7477 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 0.9653 0.9856 1.0251 1.1128 1.3449 2.0965 2.7527 2.9608 3.012 3.0177 3.0143 3.0103 3.0079 3.0062 u2 2.7901 2.9261 3.0106 3.0821 3.2917 4.1039 4.811 5.0404 5.0984 5.0934 5.0717 5.0526 5.0399 5.0306 u3 2.88 3.0661 3.2252 3.4662 4.0382 5.5877 6.8118 7.2066 7.2996 7.2675 7.2034 7.15 7.1134 7.0869 u4 4.8939 5.0926 5.2509 5.436 5.9941 7.7231 9.1364 9.6073 9.6907 9.5882 9.4452 9.3304 9.2506 9.1924 u5 5.5283 5.7961 6.055 6.5161 7.5736 9.9317 11.7532 12.3202 12.3438 12.1129 11.8432 11.6313 11.4811 11.3712 u6 7.8908 8.2396 8.4806 8.8492 9.9513 12.7737 14.9274 15.4938 15.3648 14.9271 14.4683 14.1107 13.8529 13.661 u7 10.5917 11.0972 11.3853 11.7713 13.0322 16.4337 18.9135 19.3674 18.9636 18.2094 17.4708 16.8942 16.4697 16.1476 SNR 28 29 30 u1 3.0044 3.0038 3.003 u2 5.023 5.0178 5.0128 u3 7.067 7.0512 7.0407 u4 9.1486 9.1126 9.0893 u5 11.2883 11.2217 11.1749 u6 13.5157 13.3981 13.3164 u7 15.9014 15.7029 15.5677

c4) 256-QAM/16-PAM for the Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9798 0.9967 0.9947 0.9971 1.0007 1.03 1.0688 1.0762 1.0537 1.0342 1.0147 0.9992 0.9918 0.9922 u2 0.8908 1.0016 0.9934 1.0006 0.9987 1.0588 1.1381 1.2317 1.3585 1.5225 1.7405 2.0063 2.2615 2.4654 u3 0.9072 1.0041 0.9993 1.0003 0.9997 1.0295 1.0664 1.1441 1.2863 1.4689 1.7111 2.0037 2.2873 2.5275 u4 1.4244 2.0539 2.4036 2.6739 2.9049 3.019 3.2106 3.239 3.2891 3.4602 3.7019 3.9966 4.2761 4.5013 u5 1.3906 2.0371 2.3593 2.6731 2.9097 2.6841 2.8603 3.0627 3.3005 3.5807 3.9182 4.3056 4.6871 5.0312 u6 1.5899 2.024 2.3535 2.6762 2.8921 3.0205 3.2171 3.6521 4.2742 4.8242 5.3945 5.997 6.5483 7.0034 u7 1.6351 2.042 2.3973 2.6721 2.8859 3.9489 4.5222 5.0297 5.6081 6.271 7.0282 7.8489 8.6107 9.2424 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 0.9989 1.0259 1.1155 1.3963 1.8534 2.2282 2.4891 2.6619 2.7729 2.8437 2.889 2.9176 2.9379 2.9516 u2 2.6086 2.7135 2.8419 3.1795 3.7175 4.1541 4.4608 4.664 4.7936 4.8758 4.9257 4.956 4.9778 4.9933 u3 2.7307 2.9443 3.2659 3.9675 4.9244 5.676 6.197 6.5386 6.7531 6.8857 6.9639 7.0096 7.0412 7.064 u4 4.6692 4.8339 5.1383 5.9281 7.0475 7.9072 8.4862 8.8521 9.0685 9.1906 9.253 9.282 9.3008 9.3117 u5 5.3576 5.7413 6.3082 7.4353 8.9135 10.0292 10.7694 11.2248 11.4823 11.6157 11.6732 11.6881 11.6943 11.6904 u6 7.3828 7.7887 8.4196 9.7825 11.5726 12.8864 13.7217 14.2018 14.4402 14.5326 14.5421 14.508 14.472 14.4315 u7 9.7612 10.2938 11.0879 12.7927 15.0009 16.5632 17.5017 17.9894 18.1764 18.1926 18.1172 17.9984 17.8904 17.7896 SNR 28 29 30 31 32 33 34 35 36 37 38 39 40 u1 2.9597 2.9661 2.9708 2.9726 2.9757 2.979 2.9795 2.9803 2.981 2.982 2.9813 2.9795 2.9788 u2 4.9991 5.0047 5.0081 5.009 5.0124 5.0173 5.0145 5.016 5.0165 5.0165 5.0154 5.0085 5.0096 u3 7.0698 7.0758 7.0795 7.0795 7.0819 7.0887 7.0822 7.086 7.086 7.0867 7.0883 7.0759 7.0772 u4 9.3029 9.2996 9.2958 9.2878 9.2861 9.2921 9.2787 9.2803 9.2787 9.2784 9.2785 9.2623 9.2664 u5 11.668 11.6526 11.6385 11.6222 11.6137 11.6142 11.5969 11.5934 11.5903 11.5892 11.5893 11.5636 11.561 u6 14.3754 14.3333 14.2955 14.2621 14.2394 14.2301 14.2009 14.1909 14.1835 14.1804 14.173 14.1335 14.1421 u7 17.6749 17.5886 17.5132 17.4498 17.4048 17.3749 17.3292 17.307 17.2908 17.2734 17.2633 17.208 17.2206

d1) 1024-QAM or 32-PAM for a Non-Fading Channel (1. Option)

SNR 8 9 10 11 12 13 14 15 16 17 18 u₁ 1.0067 1.0148 1.0507 1.0476 1.0198 1.0464 1.0909 1.0037 1.0187 1.0148 1.0251 u₂ 1.0380 1.0523 1.0845 1.0835 1.0373 1.0701 1.0910 1.0428 1.0711 1.1108 1.2863 u₃ 1.0695 1.0949 1.1046 1.1376 1.0754 1.0813 1.1644 1.0447 1.0807 1.1364 1.2891 u₄ 1.6402 1.8347 2.0518 2.5314 2.6729 2.9275 3.0920 2.9924 3.0361 3.0693 3.3256 u₅ 1.6741 1.9096 2.1058 2.5742 2.7200 2.9512 3.1966 3.0105 3.0631 3.0902 3.3296 u₆ 1.6802 1.9096 2.1287 2.5742 2.7278 3.0476 3.2399 3.1832 3.3080 3.4418 3.9436 u₇ 1.7120 1.9314 2.1552 2.6395 2.7641 3.0980 3.3711 3.1850 3.3133 3.4430 3.9450 u₈ 3.7616 3.9751 4.2512 4.6900 4.7720 5.0430 5.3006 5.1666 5.2248 5.3743 5.9219 u₉ 3.7988 4.0277 4.3122 4.7622 4.8209 5.1017 5.4156 5.1666 5.2248 5.3743 5.9219 u₁₀ 3.7988 4.0671 4.3749 4.8789 5.0144 5.5053 5.8716 5.8269 5.9842 6.2741 7.2272 u₁₁ 3.8518 4.1230 4.3905 4.8870 5.0144 5.5054 5.8716 5.8763 6.0961 6.4804 7.4547 u₁₂ 4.8732 5.3269 6.0182 6.8091 7.0796 7.6797 8.0443 7.9004 7.9850 8.3476 9.4109 u₁₃ 4.9607 5.3481 6.0182 6.8466 7.0905 7.6878 8.1462 8.2883 8.3856 8.9683 10.1262 u₁₄ 5.5363 5.9883 6.7380 7.6823 8.1294 8.8170 9.3690 9.9247 10.1499 11.0046 12.4646 u₁₅ 5.7097 6.5205 7.2058 8.0785 8.4303 9.8312 10.9109 11.9003 12.0120 13.4835 15.2549 SNR 19 20 21 22 23 24 25 26 27 28 29 u₁ 1.0024 1.0006 1.0016 1.0005 1.0031 1.0346 1.2687 2.5688 2.9137 2.9903 3.0038 u₂ 1.7107 2.5479 2.8831 2.9838 3.0077 3.0243 3.2174 4.5722 4.9309 5.0103 5.0225 u₃ 1.7141 2.5515 2.8832 2.9845 3.0245 3.1135 3.6704 6.2334 6.8977 7.0454 7.0642 u₄ 3.6770 4.5909 4.9553 5.0538 5.0615 5.0609 5.4996 8.2567 8.9703 9.1297 9.1403 u₅ 3.6786 4.5909 4.9553 5.0704 5.1383 5.3184 6.3316 10.0819 11.0442 11.2591 11.2602 u₆ 4.8209 6.4238 7.0286 7.1835 7.1646 7.1593 8.0505 12.1692 13.2274 13.4612 13.4368 u₇ 4.8209 6.4274 7.0642 7.2914 7.4407 7.8023 9.3361 14.2128 15.4757 15.7441 15.6806 u₈ 6.8262 8.6260 9.3012 9.4393 9.3945 9.5457 11.0297 16.4523 17.8558 18.1316 18.0048 u₉ 6.8553 8.7222 9.5195 9.8531 10.1506 10.7731 12.6757 18.7884 20.3719 20.6408 20.4242 u₁₀ 8.6131 10.9071 11.7486 11.9625 12.0642 12.5104 14.5305 21.3353 23.0690 23.2947 22.9559 u₁₁ 8.9135 11.4255 12.5514 13.0881 13.5886 14.2704 16.5415 24.1089 25.9761 26.1177 25.6206 u₁₂ 11.0009 13.7880 14.9096 15.3045 15.6473 16.3124 18.7922 27.1742 29.1347 29.1436 28.4455 u₁₃ 11.9746 15.2957 16.9425 17.5792 17.9741 18.6433 21.3263 30.5883 32.5987 32.4209 31.4714 u₁₄ 14.5395 18.2064 19.8795 20.4586 20.7562 21.3536 24.2238 34.4505 36.4620 36.0306 34.7706 u₁₅ 17.7040 21.9252 23.6632 24.0824 24.1747 24.6202 27.6622 38.9891 40.9391 40.1627 38.5012 SNR 30 31 32 33 34 35 36 37 38 39 40 u₁ 3.0029 3.0028 3.0023 3.0037 3.0010 3.0022 2.9991 3.0009 2.9630 2.7120 2.4609 u₂ 5.0173 5.0132 5.0104 5.0116 5.0054 5.0074 5.0111 5.0049 4.9499 4.2412 3.3493 u₃ 7.0495 7.0372 7.0285 7.0273 7.0167 7.0181 7.0328 7.0073 6.9154 5.8741 4.7174 u₄ 9.1072 9.0800 9.0612 9.0527 9.0358 9.0349 9.0456 9.0153 8.8955 7.6262 6.4878 u₅ 11.1981 11.1476 11.1119 11.0933 11.0668 11.0584 11.0454 11.0325 10.8427 8.9624 7.7169 u₆ 13.3309 13.2465 13.1864 13.1515 13.1108 13.0955 13.0779 13.0621 12.7897 10.8692 8.5130 u₇ 15.5146 15.3830 15.2899 15.2330 15.1738 15.1445 15.0931 15.1013 14.7269 12.0858 9.8751 u₈ 17.7592 17.5659 17.4290 17.3407 17.2566 17.2099 17.1422 17.1488 16.6081 13.7050 11.5486 u₉ 20.0760 19.8040 19.6107 19.4829 19.3658 19.2996 19.1878 19.2029 18.5568 15.1881 12.4136 u₁₀ 22.4791 22.1087 21.8439 21.6641 21.5065 21.4089 21.2611 21.2792 20.1847 16.9468 14.2051 u₁₁ 24.9859 24.4938 24.1410 23.8963 23.6863 23.5530 23.3458 23.3490 21.2990 18.7549 15.1350 u₁₂ 27.6192 26.9793 26.5155 26.1908 25.9177 25.7334 25.4559 25.4652 24.3404 20.4199 16.3718 u₁₃ 30.4127 29.5936 28.9967 28.5657 28.2131 27.9698 27.6069 27.6293 25.1817 20.6889 18.1707 u₁₄ 33.4269 32.3855 31.6180 31.0614 30.6020 30.2801 29.8393 29.8551 28.0675 24.2726 18.9363 u₁₅ 36.7956 35.4677 34.4795 33.7493 33.1451 32.7195 32.0437 32.1466 29.1598 25.0126 20.2944

d2) 1024-QAM or 32-PAM for a Fading Channel (1. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 u₁ 1.0003 1.0000 1.0000 1.0011 1.0000 1.0000 1.0006 1.0000 1.0002 1.0043 1.0108 u₂ 1.0003 1.0049 1.0163 1.0196 1.0208 1.0308 1.0214 1.0390 1.0252 1.0803 1.1627 u₃ 1.0027 1.0254 1.0360 1.0381 1.0582 1.0725 1.0400 1.0475 1.0286 1.1088 1.1942 u₄ 1.0164 1.0686 1.1300 1.2102 1.2704 1.3984 1.4402 1.5327 1.6809 1.9443 2.2594 u₅ 1.0277 1.0704 1.1395 1.2359 1.2821 1.4126 1.4586 1.5465 1.6972 1.9733 2.3050 u₆ 1.0456 1.0894 1.1495 1.2553 1.2994 1.4417 1.4951 1.5465 1.7362 2.0279 2.4395 u₇ 1.0487 1.1132 1.1734 1.2757 1.3364 1.4849 1.5096 1.5503 1.7364 2.0560 2.4406 u₈ 1.9738 2.1671 2.3628 2.5480 2.7476 3.0647 3.1661 3.3174 3.5767 3.8954 4.3049 u₉ 2.0526 2.1986 2.4403 2.6234 2.8083 3.1166 3.2014 3.3403 3.5857 3.9143 4.3315 u₁₀ 2.0663 2.2340 2.4536 2.6234 2.8196 3.1458 3.2015 3.3860 3.6394 4.0486 4.6119 u₁₁ 2.1022 2.2898 2.5070 2.6836 2.8698 3.1887 3.2388 3.3919 3.6572 4.0846 4.6119 u₁₂ 2.4454 2.6894 2.9825 3.2145 3.4803 3.8713 4.0826 4.4221 4.8650 5.3735 6.0449 u₁₃ 2.5537 2.7750 3.0830 3.2993 3.6342 4.0375 4.1566 4.4677 4.8650 5.3735 6.1193 u₁₄ 2.7190 2.9743 3.3004 3.5711 3.9845 4.3829 4.6192 4.9832 5.4362 6.1354 6.8700 u₁₅ 2.8164 3.1340 3.3947 3.7517 4.0778 4.5240 4.8297 5.2517 5.7299 6.6103 7.5087 SNR 11 12 13 14 15 16 17 18 19 20 21 u₁ 1.0206 1.0240 1.0158 1.0030 1.0094 1.0165 1.0109 1.0003 1.0009 1.0043 1.0003 u₂ 1.0739 1.1088 1.2267 1.0173 1.0577 1.1641 1.3963 1.6842 2.0893 2.3787 2.5628 u₃ 1.1015 1.1366 1.2493 1.0173 1.0632 1.1895 1.4131 1.6863 2.0899 2.3793 2.5641 u₄ 2.3031 2.5070 2.7823 2.6207 2.7531 2.9022 3.1798 3.5239 3.9928 4.3337 4.5385 u₅ 2.3307 2.5226 2.8092 2.6267 2.7580 2.9222 3.1944 3.5282 3.9930 4.3342 4.5580 u₆ 2.3962 2.6229 3.0150 2.7411 2.9810 3.3589 3.9199 4.5765 5.3853 5.9529 6.2800 u₇ 2.4238 2.6526 3.0349 2.7470 2.9811 3.3605 3.9203 4.5765 5.3906 5.9865 6.3991 u₈ 4.3380 4.5737 4.9461 4.6738 4.8680 5.2293 5.8532 6.6194 7.5215 8.1146 8.4195 u₉ 4.3743 4.6127 4.9764 4.6738 4.8680 5.2293 5.8532 6.6415 7.6038 8.3211 8.8558 u₁₀ 4.6129 4.9434 5.4050 5.3030 5.6793 6.3007 7.1684 8.1999 9.3413 10.1083 10.5973 u₁₁ 4.6129 4.9434 5.4050 5.3190 5.7268 6.4114 7.3330 8.5123 9.8455 10.8886 11.6792 u₁₂ 6.2332 6.6912 7.1932 7.0781 7.4631 8.1246 9.1671 10.4955 11.9313 12.9749 13.7196 u₁₃ 6.2378 6.7067 7.2143 7.4316 7.8792 8.7397 9.9527 11.6664 13.4007 14.6947 15.6090 u₁₄ 7.2044 7.7531 8.3908 9.0011 9.5503 10.5383 11.9678 13.9641 15.9024 17.3089 18.2685 u₁₅ 7.8925 8.6732 9.0513 10.9148 11.5100 12.7890 14.4376 16.9300 19.1680 20.7369 21.7475 SNR 22 23 24 25 26 27 28 29 30 31 32 u₁ 1.0002 1.0753 1.5871 2.0792 2.3953 2.5979 2.7284 2.8108 2.8638 2.8972 2.9205 u₂ 2.6821 2.8032 3.3595 3.9137 4.2801 4.5188 4.6763 4.7770 4.8432 4.8844 4.9121 u₃ 2.6985 2.9606 4.0489 5.0644 5.7316 6.1639 6.4450 6.6243 6.7411 6.8116 6.8624 u₄ 4.6475 4.8124 5.9653 7.0563 7.7599 8.2091 8.4995 8.6815 8.7991 8.8675 8.9155 u₅ 4.7447 5.1854 6.8626 8.3577 9.3324 9.9565 10.3588 10.6098 10.7698 10.8617 10.9265 u₆ 6.4363 6.7835 8.6319 10.2875 11.3529 12.0290 12.4603 12.7241 12.8892 12.9778 13.0422 u₇ 6.7723 7.5030 9.8196 11.8295 13.1294 13.9541 14.4760 14.7917 14.9857 15.0876 15.1596 u₈ 8.6146 9.2375 11.8029 14.0035 15.3949 16.2563 16.7886 17.0983 17.2797 17.3649 17.4228 u₉ 9.3840 10.3216 13.3049 15.8351 17.4372 18.4233 19.0262 19.3679 19.5628 19.6463 19.6994 u₁₀ 11.0496 12.0123 15.3459 18.1385 19.8764 20.9233 21.5442 21.8783 22.0561 22.1145 22.1450 u₁₁ 12.3712 13.5373 17.2964 20.4157 22.3392 23.4820 24.1409 24.4781 24.6459 24.6783 24.6849 u₁₂ 14.3775 15.6118 19.8018 23.2294 25.2925 26.4779 27.1285 27.4264 27.5506 27.5290 27.4931 u₁₃ 16.3759 17.7521 22.4374 26.2246 28.4576 29.7039 30.3509 30.6108 30.6865 30.6041 30.5122 u₁₄ 19.0535 20.5285 25.7859 29.9638 32.3556 33.6202 34.2212 34.3969 34.3835 34.2046 34.0347 u₁₅ 22.5334 24.1205 30.0937 34.7506 37.3202 38.5786 39.0930 39.1396 38.9925 38.6816 38.3850 SNR 33 34 35 36 37 38 39 40 u₁ 2.9354 2.9461 2.9539 2.9566 2.9625 2.9679 2.9706 2.9668 u₂ 4.9294 4.9430 4.9521 4.9535 4.9610 4.9733 4.9711 4.9647 u₃ 6.8891 6.9128 6.9279 6.9327 6.9441 6.9639 6.9598 6.9537 u₄ 8.9381 8.9612 8.9734 8.9760 8.9857 9.0117 9.0034 8.9914 u₅ 10.9554 10.9880 11.0022 11.0031 11.0166 11.0516 11.0381 11.0244 u₆ 13.0641 13.0956 13.1054 13.1036 13.1132 13.1541 13.1339 13.1153 u₇ 15.1815 15.2131 15.2214 15.2164 15.2267 15.2711 15.2475 15.2256 u₈ 17.4273 17.4495 17.4469 17.4330 17.4369 17.4818 17.4503 17.4219 u₉ 19.6952 19.7108 19.6985 19.6773 19.6762 19.7216 19.6855 19.6521 u₁₀ 22.1170 22.1128 22.0880 22.0535 22.0433 22.0913 22.0378 21.9943 u₁₁ 24.6327 24.6090 24.5689 24.5179 24.4941 24.5412 24.4762 24.4209 u₁₂ 27.3953 27.3392 27.2667 27.1957 27.1547 27.1976 27.1095 27.0355 u₁₃ 30.3630 30.2747 30.1682 30.0651 30.0017 30.0359 29.9279 29.8362 u₁₄ 33.8099 33.6615 33.5079 33.3683 33.2557 33.2767 33.1414 33.0224 u₁₅ 38.0516 37.8298 37.6071 37.3990 37.2354 37.2407 37.0845 36.9002 SNR 42 44 46 48 50 u₁ 2.9738 2.9727 2.9803 2.9747 2.9755 u₂ 4.9763 4.9704 4.9831 4.9798 4.9849 u₃ 6.9716 6.9620 6.9761 6.9699 6.9855 u₄ 9.0140 8.9995 9.0169 9.0005 9.0175 u₅ 11.0516 11.0383 11.0596 11.0277 11.0471 u₆ 13.1460 13.1331 13.1545 13.0993 13.1231 u₇ 15.2595 15.2451 15.2638 15.1874 15.2293 u₈ 17.4578 17.4387 17.4605 17.3555 17.4128 u₉ 19.6900 19.6695 19.6999 19.5662 19.6282 u₁₀ 22.0331 22.0039 22.0346 21.8900 21.9543 u₁₁ 24.4634 24.4247 24.4522 24.2985 24.3779 u₁₂ 27.0712 27.0228 27.0504 26.8712 26.9537 u₁₃ 29.8692 29.7967 29.8201 29.6120 29.6794 u₁₄ 33.0482 32.9359 32.9517 32.7729 32.8541 u₁₅ 36.8842 36.7255 36.7204 36.5908 36.7169

d3) 1024-QAM/32-PAM for a Non-Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9992 0.9991 0.9626 0.9967 0.9967 0.9988 0.9997 1.0671 1.0969 1.0363 0.962 1.0001 0.9878 0.9942 u2 0.9957 0.9942 0.8697 0.9895 0.9965 0.9992 0.9989 1.1388 1.2043 1.2107 1.1702 0.9997 0.9747 0.966 u3 0.9965 0.9943 0.8971 0.99 0.9962 0.9991 0.9986 1.0674 1.0955 1.1639 1.2161 0.9996 0.9863 0.9719 u4 0.9971 0.9965 0.6648 0.99 0.9954 0.9994 1.0008 1.1386 1.2048 1.3562 1.4866 1.8264 2.2272 2.5533 u5 0.996 0.9939 0.6491 0.9905 0.9956 0.9997 1.001 1.2138 1.3242 1.4129 1.4414 1.848 2.2217 2.5387 u6 0.9992 1.0019 0.6995 0.9974 0.9977 0.9998 1.0017 1.1384 1.2058 1.2085 1.1751 1.8267 2.223 2.5691 u7 0.9999 1.0022 0.719 0.9994 0.9993 1.0004 1.0017 1.0667 1.0964 1.162 1.2213 1.8066 2.2286 2.581 u8 1.0018 1.0047 0.9796 2.2704 2.8447 3.3339 3.6691 4.1038 4.3038 4.1189 3.88 3.962 4.3457 4.661 u9 1.0009 1.0043 0.9448 2.264 2.8416 3.334 3.6696 3.6418 3.8694 4.0902 4.1993 4.1097 4.4994 4.7046 u10 0.9975 0.9957 0.8525 2.2387 2.8354 3.336 3.672 3.4119 3.666 3.7746 3.802 4.2647 4.7161 5.1202 u11 0.9986 0.9982 0.8839 2.2405 2.8378 3.3375 3.6721 3.6428 3.8684 3.7435 3.6203 4.1131 4.5362 5.0343 u12 0.9986 0.9963 1.2974 2.2393 2.8414 3.3349 3.6662 4.1042 4.3048 4.1203 3.8917 6.185 6.9957 7.2365 u13 0.9975 0.996 1.243 2.2388 2.838 3.3348 3.6674 3.6422 3.8687 4.0904 4.2129 5.8337 6.7509 7.454 u14 1.001 1.0011 1.4137 2.2601 2.844 3.335 3.6673 4.1032 4.3066 5.0379 5.5707 6.2198 7.2075 8.594 u15 1.0017 1.0022 1.4853 2.2698 2.8465 3.3339 3.6669 6.1624 6.9359 7.2501 7.4066 8.6211 9.7438 10.859 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 1.0007 1.0027 0.9981 0.9933 0.9936 0.999 1 1.0001 0.9973 1.0036 1.0338 1.2685 2.568 2.9124 u2 0.9694 0.9834 1.0086 1.0594 1.2188 1.7124 2.5469 2.8781 2.9836 3.0078 3.024 3.2172 4.5709 4.9289 u3 0.9681 0.9811 1.0101 1.0676 1.2263 1.7139 2.5465 2.8764 2.9837 3.0244 3.1126 3.6704 6.2313 6.8942 u4 2.7737 2.9007 2.9741 3.0241 3.159 3.6872 4.5907 4.9456 5.0494 5.0625 5.0597 5.4996 8.2546 8.9668 u5 2.7714 2.9125 2.9988 3.0553 3.1727 3.6864 4.5862 4.9442 5.0663 5.138 5.3175 6.3322 10.0797 11.0396 u6 2.8418 3.0307 3.1789 3.35 3.7479 4.8324 6.417 7.0146 7.1785 7.1643 7.1579 8.0513 12.1665 13.2221 u7 2.846 3.0218 3.1519 3.3116 3.7215 4.8226 6.4211 7.0502 7.2858 7.4383 7.8018 9.3367 14.2096 15.4697 u8 4.9072 5.0916 5.2328 5.352 5.6798 6.8426 8.6195 9.2808 9.4323 9.3928 9.5449 11.0304 16.4487 17.8497 u9 4.8825 5.0325 5.1573 5.2795 5.6568 6.8702 8.7174 9.4992 9.8449 10.1481 10.7709 12.6768 18.7845 20.3652 u10 5.4415 5.6696 5.8553 6.1215 6.9014 8.6299 10.8957 11.7222 11.9532 12.0621 12.5094 14.5322 21.3307 23.0612 u11 5.45 5.7667 6.0273 6.3484 7.1423 8.9474 11.4173 12.5228 13.0769 13.586 14.2684 16.5436 24.1032 25.9674 u12 7.6047 7.8958 8.1046 8.3161 9.0363 11.0231 13.7773 14.8757 15.2913 15.6441 16.3101 18.7948 27.1676 29.1243 u13 8.0146 8.4122 8.6722 8.9298 9.7542 12.0148 15.2835 16.9016 17.5633 17.972 18.6404 21.3291 30.5806 32.5873 u14 9.6267 10.3424 10.7968 11.1339 12.0444 14.5782 18.1947 19.8327 20.4394 20.7517 21.3511 24.2271 34.4413 36.4503 u15 11.9177 12.7867 13.3749 13.7814 14.8151 17.7532 21.9096 23.606 24.0612 24.1702 24.6165 27.6663 38.9792 40.9267 SNR 28 29 30 31 32 33 34 35 36 37 38 39 40 u1 2.9902 3.0016 3.0038 3.002 3.0024 3.0017 3.0014 3.0014 2.9988 3.0102 3.0035 2.7197 2.0472 u2 5.01 5.0206 5.0186 5.0131 5.0105 5.0084 5.006 5.0051 5.0006 5.0192 5.0363 4.4139 2.9841 u3 7.0446 7.0618 7.0515 7.0373 7.0287 7.022 7.0169 7.0134 7.0044 7.0244 7.0893 6.2809 3.9607 u4 9.1283 9.1368 9.1105 9.0811 9.0608 9.0466 9.0367 9.0261 9.0134 9.0332 9.1092 7.9322 5.0898 u5 11.257 11.2562 11.2029 11.1486 11.1121 11.0856 11.0685 11.0475 11.0277 11.0421 11.1317 9.6412 6.0761 u6 13.4588 13.4329 13.3374 13.2478 13.1867 13.143 13.1106 13.0776 13.0484 13.061 13.1503 11.2735 7.1638 u7 15.7417 15.6758 15.5224 15.3852 15.2907 15.2225 15.173 15.1242 15.0767 15.0837 15.1749 13.1326 8.1645 u8 18.1292 18.0006 17.7684 17.5682 17.4293 17.3297 17.2569 17.1873 17.1224 17.1191 17.2333 14.826 9.3331 u9 20.6379 20.419 20.0868 19.8058 19.6109 19.4704 19.3651 19.2702 19.1868 19.1703 19.3081 16.4589 10.3444 u10 23.2916 22.9487 22.4913 22.1116 21.8445 21.6501 21.5069 21.3796 21.2695 21.2328 21.3472 18.0904 11.3035 u11 26.1151 25.6105 24.9996 24.4967 24.1418 23.8821 23.6873 23.5173 23.3768 23.3264 23.4267 19.7596 12.4831 u12 29.1412 28.4332 27.6343 26.9825 26.5176 26.1751 25.9187 25.6964 25.5123 25.421 25.4868 21.3998 13.6002 u13 32.4176 31.4579 30.4306 29.5967 28.997 28.5515 28.2162 27.9277 27.6916 27.5544 27.5728 23.1872 14.6124 u14 36.0267 34.7541 33.4466 32.3882 31.6189 31.0443 30.605 30.2317 29.932 29.7649 29.6897 24.9174 15.8244 u15 40.1583 38.4818 36.8177 35.4703 34.4789 33.7311 33.1542 32.6692 32.2795 32.0045 31.9429 26.7754 16.8182

d4) 1024-QAM/32-PAM for a Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9877 0.9983 1.0021 0.996 1.0038 1.0274 1.0458 1.0252 1.0251 1.0106 1.0022 0.9999 0.9993 0.9997 u2 0.9503 0.9963 0.9924 1.001 0.9979 1.0502 1.1021 1.093 1.0684 1.0421 1.0226 1.0034 0.9938 0.9916 u3 0.9615 0.9958 0.9968 0.9963 1.0033 1.0263 1.0508 1.0681 1.0408 1.0311 1.0201 1.0037 0.9938 0.9911 u4 0.8564 0.9951 0.9982 0.9969 1.0019 1.0506 1.1052 1.2121 1.3282 1.4929 1.7209 1.983 2.2325 2.4349 u5 0.8494 0.9967 0.994 0.9991 1.0008 1.073 1.1571 1.2411 1.3645 1.5094 1.7258 1.9826 2.2312 2.4346 u6 0.8807 0.9994 0.9998 0.9959 1.0025 1.0482 1.1021 1.1634 1.3105 1.4612 1.6899 1.9706 2.2471 2.486 u7 0.8914 1.0007 0.9995 0.998 0.9995 1.0236 1.0521 1.1359 1.2768 1.4444 1.6851 1.9712 2.2486 2.4864 u8 1.3814 2.0455 2.4146 2.6684 2.9175 3.2588 3.4859 3.2744 3.2804 3.4275 3.6722 3.954 4.2289 4.4576 u9 1.3622 2.044 2.4 2.6704 2.8872 2.8611 3.0858 3.2456 3.3136 3.4906 3.7323 3.9988 4.255 4.4646 u10 1.2981 2.0293 2.3562 2.6608 2.8918 2.6571 2.8799 3.0861 3.3236 3.5804 3.9166 4.2842 4.6461 4.9706 u11 1.3174 2.0299 2.3711 2.6666 2.9157 2.8566 3.0645 3.0951 3.294 3.5187 3.8461 4.2212 4.6016 4.9552 u12 1.5422 2.0304 2.3575 2.6702 2.919 3.2583 3.4956 3.7397 4.4647 4.8383 5.3122 5.8215 6.3089 6.7222 u13 1.5175 2.0313 2.3446 2.6653 2.8934 2.8625 3.0965 3.6125 4.257 4.7767 5.3692 5.9729 6.5416 7.0327 u14 1.604 2.0428 2.3901 2.6689 2.8884 3.265 3.5501 4.3656 4.7788 5.4497 6.2546 7.0898 7.8656 8.5382 u15 1.6294 2.0466 2.4075 2.6719 2.9129 4.5146 5.143 5.676 6.3035 6.969 7.8139 8.7306 9.6322 10.4411 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 1.0006 1.0003 0.9986 0.9994 0.9989 1.0005 0.9993 1.0023 1.0042 1.0772 1.5857 2.0789 2.3946 2.5983 u2 0.9966 1.0149 1.0776 1.2742 1.6871 2.0897 2.3726 2.5667 2.6852 2.8011 3.3587 3.9147 4.2782 4.5193 u3 0.9957 1.0158 1.0779 1.2749 1.6874 2.0888 2.3722 2.5683 2.7063 2.9634 4.0473 5.0664 5.7293 6.1649 u4 2.5818 2.6848 2.7905 3.0323 3.5222 3.9945 4.3233 4.5468 4.6563 4.8127 5.9637 7.0579 7.7572 8.2107 u5 2.5854 2.6903 2.7982 3.0371 3.522 3.9931 4.325 4.5636 4.7536 5.1864 6.8591 8.3596 9.3297 9.9594 u6 2.6894 2.882 3.1454 3.6813 4.5789 5.3843 5.9387 6.2876 6.4513 6.7838 8.6281 10.2901 11.3497 12.0321 u7 2.6871 2.8747 3.1351 3.6718 4.5753 5.3894 5.9728 6.4073 6.786 7.5029 9.816 11.834 13.1252 13.9574 u8 4.6338 4.7815 5.0115 5.5854 6.6178 7.5206 8.0948 8.4282 8.6367 9.238 11.7978 14.0092 15.3897 16.2598 u9 4.6222 4.7619 4.9912 5.5804 6.6403 7.6013 8.3014 8.8692 9.4056 10.32 13.3009 15.8419 17.4299 18.4269 u10 5.2658 5.5779 6.0174 6.8559 8.1969 9.3371 10.0842 10.6112 11.0768 12.0115 15.3408 18.1472 19.8671 20.9273 u11 5.2889 5.6434 6.134 7.0475 8.5126 9.8429 10.8635 11.6946 12.4 13.5356 17.2901 20.4243 22.3301 23.4863 u12 7.0625 7.3854 7.8549 8.8436 10.4887 11.9255 12.9446 13.7334 14.4128 15.6099 19.7947 23.2381 25.2825 26.4823 u13 7.4575 7.8797 8.4919 9.7042 11.6571 13.3962 14.6601 15.6274 16.4161 17.7524 22.4306 26.2322 28.4484 29.7085 u14 9.1068 9.635 10.344 11.727 13.9522 15.8981 17.2695 18.2933 19.0986 20.5256 25.7783 29.973 32.3413 33.6247 u15 11.14 11.7874 12.6414 14.2894 16.9161 19.1591 20.6892 21.7769 22.5894 24.1254 30.084 34.7629 37.3028 38.5854 SNR 28 29 30 31 32 33 34 35 36 37 38 39 40 u1 2.7301 2.8111 2.8638 2.8985 2.9204 2.9359 2.9464 2.9538 2.959 2.9627 2.9646 2.9686 2.9708 u2 4.6776 4.7777 4.8422 4.8846 4.9112 4.9307 4.9428 4.952 4.9581 4.9636 4.9649 4.9695 4.9721 u3 6.4472 6.6249 6.7392 6.8128 6.8596 6.8928 6.913 6.9288 6.9398 6.9487 6.951 6.9583 6.9643 u4 8.5011 8.6817 8.7961 8.8683 8.9124 8.9438 8.9619 8.9752 8.9849 8.9938 8.9932 9.0001 9.0054 u5 10.3587 10.6081 10.7659 10.8639 10.9225 10.9642 10.9877 11.0041 11.0164 11.0274 11.0264 11.0342 11.0416 u6 12.4587 12.7205 12.8844 12.9827 13.0371 13.0761 13.095 13.1067 13.1177 13.1268 13.1229 13.1289 13.1362 u7 14.4744 14.7859 14.98 15.0938 15.153 15.1954 15.2147 15.2242 15.2319 15.2421 15.2363 15.2411 15.2498 u8 16.7868 17.0907 17.2736 17.3718 17.4153 17.4442 17.4504 17.4501 17.4511 17.4547 17.4418 17.4433 17.4518 u9 19.0243 19.3589 19.5552 19.6555 19.6923 19.7141 19.7134 19.7042 19.6989 19.698 19.6791 19.6776 19.6851 u10 21.5442 21.8683 22.0472 22.1242 22.1375 22.138 22.1179 22.0915 22.0748 22.0635 22.0342 22.0291 22.033 u11 24.1421 24.467 24.6335 24.688 24.6782 24.6569 24.6156 24.5739 24.5418 24.5191 24.4785 24.4679 24.468 u12 27.1288 27.4152 27.5337 27.5378 27.4826 27.4215 27.3471 27.2736 27.2191 27.1778 27.119 27.0996 27.0922 u13 30.3512 30.5985 30.6651 30.6154 30.503 30.398 30.2838 30.1761 30.0938 30.0323 29.9512 29.9185 29.8979 u14 34.2179 34.3818 34.3579 34.2186 34.0203 33.8444 33.6739 33.5132 33.3876 33.2927 33.1818 33.1313 33.0899 u15 39.0866 39.1219 38.9603 38.6961 38.3675 38.0938 37.8319 37.5978 37.4117 37.2731 37.1096 37.0386 36.9652

e1) 4096-QAM or 64-PAM for a Non-Fading Channel (1. Option)

SNR 8 9 10 11 12 13 14 15 16 17 18 u₁ 1.0009 1.0095 1.0017 1.0005 1.0026 1.0357 1.0462 1.0088 1.0294 1.0550 1.0814 u₂ 1.0034 1.0191 1.0071 1.0103 1.0058 1.0935 1.0747 1.0271 1.0589 1.1067 1.1275 u₃ 1.0085 1.0328 1.0104 1.0195 1.0178 1.1234 1.1266 1.0514 1.1024 1.1932 1.2000 u₄ 1.0271 1.0685 1.0379 1.0755 1.1253 1.2903 1.2950 1.3224 1.3806 1.9358 2.5877 u₅ 1.0425 1.0933 1.0515 1.0862 1.1495 1.3104 1.3388 1.3527 1.4228 1.9850 2.6735 u₆ 1.0680 1.1256 1.0680 1.0948 1.1750 1.3332 1.3865 1.3620 1.4469 2.0585 2.7203 u₇ 1.0914 1.1453 1.0851 1.1268 1.1974 1.3824 1.4096 1.3754 1.4702 2.1306 2.7772 u₈ 1.6408 1.9406 2.1732 2.4538 2.7812 3.2032 3.3168 3.3215 3.4226 4.0242 4.7576 u₉ 1.6739 1.9863 2.2032 2.4732 2.8165 3.2260 3.3652 3.3288 3.4528 4.1132 4.8002 u₁₀ 1.7194 2.0417 2.2381 2.5159 2.8342 3.2727 3.4215 3.3467 3.4850 4.1566 4.8626 u₁₁ 1.7336 2.0649 2.2482 2.5421 2.8665 3.3094 3.4483 3.3743 3.5120 4.2105 4.9374 u₁₂ 1.7336 2.0649 2.2482 2.5654 2.9673 3.4823 3.6899 3.7007 3.9353 5.0951 6.3475 u₁₃ 1.7489 2.0891 2.2680 2.5736 2.9882 3.5109 3.7310 3.7351 3.9752 5.1790 6.4107 u₁₄ 1.7667 2.1100 2.2697 2.5749 2.9882 3.5472 3.7653 3.7530 4.0006 5.2035 6.4781 u₁₅ 1.7858 2.1333 2.2705 2.5880 2.9954 3.6091 3.7893 3.7599 4.0301 5.3100 6.5484 u₁₆ 3.7227 4.1178 4.3166 4.6107 4.9833 5.5502 5.7186 5.6573 5.9066 7.1262 8.4751 u₁₇ 3.7418 4.1491 4.3322 4.6276 4.9903 5.5822 5.7506 5.6655 5.9204 7.2088 8.5684 u₁₈ 3.7590 4.1737 4.3574 4.6571 5.0237 5.6385 5.8167 5.6849 5.9370 7.2417 8.5939 u₁₉ 3.7960 4.2200 4.3712 4.6746 5.0441 5.6775 5.8728 5.7212 5.9817 7.2914 8.6700 u₂₀ 3.8009 4.2440 4.4357 4.8048 5.2639 6.0310 6.3672 6.3727 6.8343 8.5615 10.3314 u₂₁ 3.8124 4.2614 4.4461 4.8333 5.2981 6.0708 6.4211 6.4165 6.8835 8.6242 10.4036 u₂₂ 3.8523 4.2874 4.4500 4.8427 5.3090 6.0708 6.4211 6.4165 6.9279 8.7014 10.5216 u₂₃ 3.8737 4.3357 4.4807 4.8543 5.3363 6.1026 6.4513 6.4233 6.9731 8.8015 10.5873 u₂₄ 4.8434 5.5231 5.8999 6.5381 7.2235 8.1484 8.5019 8.3784 8.8105 10.5696 12.5476 u₂₅ 4.9258 5.5864 5.9652 6.5983 7.2684 8.1872 8.5620 8.4081 8.8693 10.6847 12.6596 u₂₆ 4.9451 5.6415 5.9778 6.5984 7.2774 8.2065 8.5897 8.4766 9.1103 11.0060 13.0289 u₂₇ 5.0309 5.7430 6.0828 6.6419 7.3205 8.2309 8.6088 8.4887 9.1104 11.0060 13.0289 u₂₈ 5.4098 6.2244 6.6305 7.3617 8.0157 9.2080 9.7789 9.9190 10.7495 12.8951 15.2014 u₂₉ 5.5000 6.3459 6.7055 7.4383 8.1449 9.3149 9.8518 9.9298 10.7503 12.8995 15.2179 u₃₀ 5.7152 6.5427 7.0184 7.8330 8.6100 9.8433 10.6486 10.6096 11.8462 13.9129 16.3707 u₃₁ 5.8780 6.7570 7.2858 8.0687 8.7350 10.1300 10.9482 10.8858 12.3898 14.9464 17.4057 SNR 19 20 21 22 23 24 25 26 27 28 29 u₁ 1.0483 1.0007 1.0044 1.0055 1.0013 1.0009 1.0008 1.0004 1.0002 1.0009 1.0000 u₂ 1.0613 1.0233 1.0049 1.0067 1.0042 1.0169 1.1155 2.1473 2.7977 2.9554 2.9938 u₃ 1.0869 1.0300 1.0156 1.0126 1.0156 1.0172 1.1158 2.1476 2.7982 2.9562 2.9938 u₄ 2.3556 2.7238 2.9064 2.9831 3.0040 3.0164 3.0800 4.1326 4.8095 4.9735 5.0126 u₅ 2.3688 2.7327 2.9092 2.9851 3.0143 3.0175 3.0803 4.1329 4.8098 4.9740 5.0127 u₆ 2.4071 2.7463 2.9108 2.9891 3.0189 3.0684 3.3125 5.4313 6.6706 6.9751 7.0470 u₇ 2.4309 2.7844 2.9252 2.9939 3.0209 3.0687 3.3127 5.4321 6.6709 6.9755 7.0476 u₈ 4.4042 4.7555 4.9733 5.0568 5.0728 5.0540 5.1743 7.3914 8.7230 9.0520 9.1240 u₉ 4.4505 4.7853 4.9821 5.0665 5.0763 5.0545 5.1744 7.3919 8.7232 9.0521 9.1269 u₁₀ 4.4768 4.8087 4.9864 5.0786 5.1205 5.2247 5.6985 8.9330 10.7048 11.1492 11.2396 u₁₁ 4.4984 4.8151 4.9894 5.0804 5.1241 5.2259 5.6990 8.9335 10.7052 11.1499 11.2521 u₁₂ 6.0304 6.6746 7.0482 7.1894 7.1853 7.1332 7.4320 10.9015 12.8463 13.3324 13.4094 u₁₃ 6.0394 6.7008 7.0583 7.1926 7.1891 7.1344 7.4326 10.9021 12.8463 13.3372 13.4549 u₁₄ 6.0730 6.7081 7.0832 7.2853 7.3954 7.6181 8.4317 12.7115 15.0078 15.5775 15.6226 u₁₅ 6.1073 6.7375 7.0832 7.2884 7.4045 7.6184 8.4328 12.7116 15.0103 15.6018 15.7683 u₁₆ 8.1524 8.8607 9.3063 9.4515 9.4026 9.4234 10.0879 14.7765 17.3133 17.9142 17.8813 u₁₇ 8.1720 8.8962 9.3102 9.4574 9.4108 9.4236 10.0879 14.7780 17.3310 18.0102 18.2795 u₁₈ 8.2313 8.9543 9.4881 9.7987 10.0367 10.4715 11.5465 16.8714 19.7069 20.3186 20.2643 u₁₉ 8.2425 8.9679 9.4972 9.8026 10.0398 10.4715 11.5513 16.8932 19.7984 20.6313 21.1418 u₂₀ 10.1358 11.0877 11.6875 11.9433 11.9948 12.2390 13.2621 19.1416 22.2235 22.8444 23.0106 u₂₁ 10.2083 11.1511 11.7122 11.9433 11.9948 12.2473 13.3038 19.2585 22.5518 23.6444 24.4435 u₂₂ 10.4647 11.5011 12.3809 12.9249 13.3478 13.8662 15.0350 21.5237 24.8994 25.7504 26.2833 u₂₃ 10.4667 11.5016 12.3809 12.9352 13.3886 13.9623 15.2365 21.9595 25.7968 27.2622 28.0976 u₂₄ 12.5892 13.7714 14.6800 15.1061 15.3331 15.7560 16.9792 24.1820 28.0789 29.3444 30.1001 u₂₅ 12.5892 13.7714 14.6898 15.2127 15.5317 16.1253 17.6049 25.3100 29.8341 31.4219 32.2373 u₂₆ 13.4094 14.7156 16.2278 17.0434 17.4121 17.9163 19.3517 27.5432 32.1791 33.7649 34.5644 u₂₇ 13.6158 15.0373 16.6096 17.6500 18.1533 18.9388 20.7325 29.6202 34.6720 36.3392 37.0984 u₂₈ 15.7576 17.2752 18.8400 19.7714 20.1992 20.8666 22.6401 32.1698 37.5238 39.2039 39.8717 u₂₉ 16.4104 18.0503 19.8935 21.3735 22.0959 22.9213 24.8156 35.1006 40.7639 42.4017 42.9261 u₃₀ 18.5684 20.5641 22.6573 24.0450 24.6870 25.4664 27.4064 38.5288 44.4858 46.0196 46.3385 u₃₁ 21.1733 23.6230 26.0750 27.5013 27.9919 28.6401 30.5717 42.6611 48.9075 50.2608 50.2913 SNR 30 31 32 33 34 35 36 37 38 39 40 u₁ 1.0001 1.0248 2.4408 2.8945 2.9839 2.9994 3.0018 3.0006 3.0003 3.0001 2.9997 u₂ 3.0017 3.0182 4.4380 4.8985 4.9886 5.0033 5.0058 5.0032 5.0024 5.0018 5.0008 u₃ 3.0030 3.0632 5.9156 6.8070 6.9830 7.0115 7.0140 7.0089 7.0069 7.0048 7.0037 u₄ 5.0173 5.0328 7.9059 8.8226 9.0024 9.0302 9.0288 9.0193 9.0151 9.0102 9.0071 u₅ 5.0216 5.1327 9.4507 10.7591 11.0195 11.0577 11.0516 11.0358 11.0282 11.0193 11.0115 u₆ 7.0498 7.0422 11.4357 12.7957 13.0656 13.0993 13.0845 13.0595 13.0468 13.0326 13.0195 u₇ 7.0641 7.2652 13.0665 14.7736 15.1170 15.1551 15.1295 15.0921 15.0721 15.0515 15.0306 u₈ 9.1060 9.0644 15.0535 16.8418 17.2002 17.2304 17.1884 17.1352 17.1049 17.0757 17.0463 u₉ 9.1497 9.5244 16.7818 18.8755 19.2998 19.3267 19.2631 19.1895 19.1460 19.1067 19.0675 u₁₀ 11.1813 11.1850 18.7842 20.9896 21.4336 21.4475 21.3554 21.2573 21.1971 21.1455 21.0958 u₁₁ 11.3033 11.9919 20.6171 23.0931 23.5947 23.5943 23.4675 23.3400 23.2595 23.1929 23.1300 u₁₂ 13.2745 13.5314 22.6537 25.2693 25.7957 25.7708 25.6021 25.4389 25.3346 25.2505 25.1715 u₁₃ 13.5814 14.6560 24.5978 27.4601 28.0325 27.9792 27.7614 27.5562 27.4240 27.3180 27.2219 u₁₄ 15.4281 16.1335 26.6926 29.7208 30.3180 30.2241 29.9475 29.6937 29.5290 29.3975 29.2822 u₁₅ 16.0896 17.4553 28.7584 32.0195 32.6497 32.5080 32.1630 31.8534 31.6506 31.4900 31.3522 u₁₆ 17.8031 18.9459 30.9410 34.3908 35.0362 34.8341 34.4104 34.0374 33.7912 33.5976 33.4333 u₁₇ 18.9158 20.3994 33.1475 36.8221 37.4807 37.2058 36.6926 36.2478 35.9521 35.7214 35.5286 u₁₈ 20.5417 21.9560 35.4574 39.3347 39.9907 39.6274 39.0134 38.4877 38.1359 37.8626 37.6368 u₁₉ 21.9857 23.5351 37.8330 41.9281 42.5704 42.1029 41.3762 40.7588 40.3444 40.0228 39.7614 u₂₀ 23.6361 25.2008 40.3158 44.6167 45.2248 44.6370 43.7840 43.0657 42.5801 42.2047 41.9019 u₂₁ 25.2935 26.9290 42.9015 47.4057 47.9613 47.2349 46.2412 45.4110 44.8462 44.4090 44.0606 u₂₂ 27.0746 28.7504 45.6132 50.3061 50.7879 49.9025 48.7528 47.7990 47.1463 46.6413 46.2405 u₂₃ 28.9429 30.6660 48.4574 53.3265 53.7113 52.6466 51.3243 50.2344 49.4838 48.9030 48.4433 u₂₄ 30.9398 32.6931 51.4505 56.4788 56.7408 55.4760 53.9630 52.7229 51.8619 51.1973 50.6724 u₂₅ 33.0715 34.8412 54.6068 59.7763 59.8883 58.4008 56.6777 55.2711 54.2893 53.5305 52.9293 u₂₆ 35.3606 37.1247 57.9431 63.2360 63.1703 61.4335 59.4783 57.8899 56.7734 55.9080 55.2244 u₂₇ 37.8240 39.5605 61.4829 66.8796 66.6073 64.5910 62.3797 60.5886 59.3222 58.3376 57.5609 u₂₈ 40.4876 42.1719 65.2585 70.7389 70.2237 67.8970 65.4018 63.3861 61.9504 60.8316 59.9460 u₂₉ 43.3896 44.9941 69.3198 74.8651 74.0651 71.3880 68.5763 66.3072 64.6797 63.4096 62.3996 u₃₀ 46.6014 48.0918 73.7587 79.3419 78.2083 75.1280 71.9563 69.3942 67.5467 66.1014 64.9470 u₃₁ 50.2840 51.6166 78.7813 84.3684 82.8265 79.2656 75.6675 72.7558 70.6393 68.9832 67.6450

e2) 4096-QAM or 64-PAM for a Fading Channel (1. Option)

SNR 10 12 14 16 18 20 22 24 26 28 30 u₁ 1.0037 1.0034 1.0348 1.0952 1.0016 1.0009 1.0005 1.0084 1.0011 1.0013 1.4601 u₂ 1.0162 1.0343 1.0617 1.1176 1.0241 1.0018 1.0036 1.4936 2.2772 2.6447 3.2217 u₃ 1.0240 1.0678 1.0884 1.1793 1.0305 1.0041 1.0043 1.4944 2.2777 2.6458 3.6969 u₄ 1.1921 1.3907 1.5640 2.0417 2.0126 2.3581 2.6689 3.2663 4.1425 4.5751 5.6208 u₅ 1.2171 1.4100 1.5873 2.1063 2.0228 2.3589 2.6691 3.2663 4.1430 4.5762 6.1651 u₆ 1.2361 1.4531 1.6033 2.1127 2.0502 2.3605 2.6803 3.8388 5.4771 6.2622 7.8852 u₇ 1.2492 1.4877 1.6363 2.1955 2.0517 2.3634 2.6818 3.8552 5.4782 6.2644 8.5434 u₈ 2.3653 2.8845 3.2972 3.9998 3.8921 4.3057 4.6463 5.7758 7.4940 8.3068 10.4374 u₉ 2.3776 2.9044 3.3210 4.0789 3.9027 4.3085 4.6470 5.7801 7.4956 8.3148 11.2098 u₁₀ 2.4146 2.9464 3.3431 4.0949 3.9258 4.3091 4.7142 6.5005 8.9584 10.0754 12.8922 u₁₁ 2.4330 2.9727 3.3727 4.1576 3.9303 4.3106 4.7159 6.5026 8.9599 10.1075 13.7819 u₁₂ 2.5921 3.2909 3.8752 5.0460 5.1105 5.9019 6.4314 8.2437 10.9416 12.1137 15.6075 u₁₃ 2.6018 3.3308 3.8838 5.1032 5.1251 5.9026 6.4322 8.2470 10.9430 12.2240 16.6372 u₁₄ 2.6036 3.3538 3.9079 5.1106 5.1577 5.9275 6.6966 9.2839 12.6130 13.9827 18.3518 u₁₅ 2.6134 3.3538 3.9575 5.2402 5.1622 5.9305 6.6977 9.2923 12.6172 14.2759 19.5480 u₁₆ 4.4724 5.2413 5.8593 7.1349 7.1838 8.0530 8.5878 11.2148 14.8247 16.1910 21.4467 u₁₇ 4.4904 5.2557 5.9016 7.2435 7.2025 8.0584 8.5900 11.2224 14.8505 16.7578 22.7923 u₁₈ 4.5233 5.2967 5.9330 7.2709 7.2402 8.2244 9.2676 12.5840 16.7154 18.3893 24.6241 u₁₉ 4.5370 5.3428 5.9400 7.3156 7.2402 8.2272 9.2676 12.5847 16.8401 19.2507 26.1464 u₂₀ 4.7553 5.7766 6.6383 8.4305 8.7991 10.0062 10.9491 14.5161 18.9533 21.0189 28.1725 u₂₁ 4.7821 5.8104 6.6641 8.4825 8.8222 10.0149 10.9503 14.5520 19.3674 22.1700 29.8997 u₂₂ 4.8082 5.8291 6.6807 8.5209 9.0392 10.6920 12.1865 16.2361 21.2176 23.9044 32.0068 u₂₃ 4.8130 5.8737 6.7033 8.6186 9.0422 10.6920 12.2150 16.4697 22.1503 25.3694 34.0023 u₂₄ 6.2441 7.4671 8.5303 10.4806 10.9914 12.7390 14.0922 18.4450 24.2033 27.3692 36.4075 u₂₅ 6.2893 7.4955 8.5634 10.5693 10.9914 12.7601 14.2864 19.1390 25.6388 29.1536 38.7203 u₂₆ 6.2893 7.5445 8.6516 10.7902 11.8153 14.1858 15.8472 20.9184 27.7224 31.3403 41.3928 u₂₇ 6.3436 7.6168 8.6551 10.7902 11.8939 14.5324 16.6065 22.3106 29.7261 33.5729 44.1720 u₂₈ 7.0226 8.5293 9.9244 12.4877 13.6889 16.4941 18.4985 24.4836 32.3433 36.2788 47.4221 u₂₉ 7.0606 8.5418 9.9244 12.4922 14.1769 17.7125 20.1454 26.6758 35.1307 39.2095 50.9584 u₃₀ 7.4057 9.0421 10.6101 13.4485 15.9473 20.0492 22.5947 29.6354 38.6833 42.8367 55.2496 u₃₁ 7.6853 9.2770 10.9700 13.9607 18.0971 23.1093 25.8301 33.4923 43.2861 47.4796 60.6968 SNR 32 34 36 38 40 42 44 u₁ 2.3630 2.7143 2.8569 2.9146 2.9430 2.9572 2.9626 u₂ 4.2240 4.6431 4.8201 4.8928 4.9295 4.9485 4.9531 u₃ 5.5916 6.3624 6.6825 6.8138 6.8769 6.9108 6.9193 u₄ 7.5711 8.3609 8.6875 8.8217 8.8852 8.9195 8.9261 u₅ 8.9677 10.1017 10.5677 10.7565 10.8452 10.8923 10.9017 u₆ 10.8558 12.0656 12.5624 12.7646 12.8566 12.9054 12.9128 u₇ 12.3100 13.8453 14.4705 14.7240 14.8372 14.8969 14.9042 u₈ 14.3495 15.9079 16.5327 16.7803 16.8878 16.9453 16.9457 u₉ 15.8626 17.7314 18.4764 18.7717 18.8959 18.9623 18.9619 u₁₀ 17.8122 19.7689 20.5381 20.8410 20.9630 21.0277 21.0190 u₁₁ 19.4002 21.6494 22.5319 22.8716 23.0051 23.0767 23.0663 u₁₂ 21.4914 23.7930 24.6692 25.0032 25.1259 25.1890 25.1683 u₁₃ 23.1749 25.7482 26.7175 27.0846 27.2145 27.2800 27.2540 u₁₄ 25.2444 27.9133 28.8962 29.2543 29.3711 29.4289 29.3923 u₁₅ 27.0554 29.9674 31.0256 31.4026 31.5200 31.5729 31.5300 u₁₆ 29.3071 32.2781 33.3164 33.6672 33.7575 33.7939 33.7339 u₁₇ 31.2488 34.4427 35.5372 35.8963 35.9772 36.0047 35.9322 u₁₈ 33.5157 36.8096 37.8974 38.2279 38.2797 38.2878 38.1965 u₁₉ 35.6233 39.1139 40.2361 40.5572 40.5894 40.5810 40.4746 u₂₀ 38.1010 41.6634 42.7477 43.0181 43.0067 42.9681 42.8356 u₂₁ 40.4118 44.1431 45.2395 45.4777 45.4325 45.3693 45.2134 u₂₂ 43.0288 46.8438 47.9000 48.0709 47.9708 47.8722 47.6880 u₂₃ 45.6116 49.5583 50.5912 50.7048 50.5545 50.4196 50.2024 u₂₄ 48.5564 52.5523 53.4949 53.5164 53.2904 53.1044 52.8455 u₂₅ 51.4802 55.5697 56.4532 56.3844 56.0878 55.8498 55.5491 u₂₆ 54.7552 58.8833 59.6566 59.4612 59.0692 58.7671 58.4167 u₂₇ 58.1823 62.3637 63.0156 62.6864 62.1896 61.8161 61.4120 u₂₈ 62.1034 66.2736 66.7414 66.2379 65.6055 65.1352 64.6642 u₂₉ 66.3748 70.5252 70.7893 70.0851 69.2959 68.7220 68.1765 u₃₀ 71.4868 75.5508 75.5368 74.5533 73.5731 72.8440 72.1957 u₃₁ 77.9207 81.8329 81.4363 80.0774 78.8139 77.8906 77.1759

e3) 4096-QAM/64-PAM for a Non-Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9997 0.9978 0.9991 1 1.0007 1.0007 1 0.9557 1.0614 0.9551 0.98 0.9906 0.9983 1.0028 u2 0.9987 0.9964 0.9907 0.9992 1.0007 1.0013 0.9998 0.9995 1.132 1.0662 0.9665 0.9929 0.9872 0.9951 u3 0.9992 0.9959 0.9909 1.0013 1.0018 1.0022 0.9998 1.0455 1.0635 1.1175 0.9872 1.0026 0.9889 0.9923 u4 0.9952 0.9939 0.9506 0.9912 0.9956 0.9997 0.9991 1.0963 1.1367 1.2469 1.0968 1.0043 0.9773 0.9706 u5 0.9949 0.9927 0.9497 0.9904 0.9958 1.0001 0.999 1.0477 1.2106 1.1914 1.0729 0.9947 0.9757 0.9733 u6 0.9959 0.9925 0.9569 0.9928 0.9977 1.0007 0.999 1.0005 1.1354 1.0632 1.0886 0.9926 0.9867 0.9808 u7 0.9964 0.9925 0.9572 0.9948 0.9985 1.0012 0.9989 1.0469 1.067 1.1141 1.1127 1.0022 0.9885 0.9781 u8 0.9979 0.996 0.82 0.9969 1.0009 1.0011 0.9982 1.0953 1.1392 1.2422 1.5245 1.8225 2.2129 2.5779 u9 0.9971 0.9926 0.8212 0.9946 0.9999 1.0006 0.9981 1.0475 1.2127 1.1856 1.4974 1.8028 2.201 2.5773 u10 0.9956 0.9897 0.8169 0.9928 0.9977 1.0004 0.998 1.0967 1.2926 1.3288 1.484 1.8262 2.1995 2.564 u11 0.9956 0.988 0.8184 0.992 0.9969 0.9997 0.9977 1.1472 1.2149 1.3855 1.5124 1.8468 2.2116 2.5645 u12 0.9999 1.0001 0.8477 1.0019 1.0015 1 0.998 1.0951 1.1374 1.2436 1.3501 1.8228 2.2139 2.5865 u13 0.9993 0.9984 0.8477 1.0004 1.0011 0.9998 0.9979 1.047 1.2107 1.1876 1.3224 1.8029 2.2021 2.5859 u14 1.0002 0.9981 0.8539 1.0011 1.0023 0.9996 0.9977 1.0003 1.1352 1.059 1.338 1.781 2.2032 2.5981 u15 1.0006 0.9988 0.8548 1.0027 1.0023 0.9993 0.9976 1.0466 1.0674 1.1096 1.365 1.7998 2.2143 2.599 u16 1.0013 0.9984 1.3062 2.2808 2.8695 3.3381 3.672 3.6931 4.5055 4.0594 3.6916 3.9511 4.3515 4.733 u17 1.0009 0.9976 1.306 2.276 2.8682 3.3383 3.6706 4.1143 4.0708 4.49 3.7952 3.9685 4.3262 4.6905 u18 1.0001 0.9975 1.2944 2.2716 2.8549 3.3373 3.668 3.692 3.8547 3.9737 3.9649 4.1043 4.4877 4.7651 u19 1.0006 0.9989 1.2962 2.2767 2.8579 3.3377 3.6688 3.4797 4.0617 3.7447 3.8381 4.0787 4.5102 4.8115 u20 0.9966 0.9843 1.2316 2.2476 2.8174 3.3366 3.6668 3.3388 3.8426 3.5963 3.7694 4.2066 4.6844 5.1505 u21 0.9965 0.9862 1.2316 2.2428 2.816 3.3366 3.6654 3.4788 3.7127 3.7506 3.8549 4.2413 4.6695 5.1004 u22 0.9979 0.9883 1.2438 2.2472 2.8316 3.338 3.6687 3.693 3.8504 3.9858 3.7378 4.1047 4.4864 4.988 u23 0.9988 0.9908 1.2452 2.2521 2.8344 3.3383 3.6697 3.4793 4.0539 3.7531 3.6629 4.0789 4.5089 5.0366 u24 0.9975 0.9885 1.5288 2.2442 2.8217 3.3383 3.6695 3.695 4.5123 4.0459 4.3425 6.0223 6.8569 7.2668 u25 0.9969 0.9892 1.527 2.2404 2.8202 3.3377 3.6672 4.1199 4.0697 4.4707 4.5777 6.3293 7.2964 7.5851 u26 0.9957 0.9906 1.5113 2.237 2.8068 3.3353 3.6622 3.6994 3.8542 3.9657 4.7092 5.9321 6.867 7.6187 u27 0.996 0.992 1.5119 2.2422 2.8098 3.3356 3.663 3.4819 4.0606 3.7388 4.5292 5.7308 6.6111 7.3641 u28 1.0002 0.9931 1.6026 2.2672 2.849 3.34 3.6708 3.6937 4.5158 4.0294 5.7423 6.024 6.8485 8.1001 u29 0.9996 0.9947 1.6004 2.264 2.8464 3.3382 3.6682 4.1221 4.0742 4.4504 5.71 6.3295 7.2893 8.6424 u30 1.0003 0.9972 1.6155 2.2689 2.86 3.3379 3.6703 6.9367 4.5402 6.1369 6.5297 7.621 8.7159 9.8487 u31 1.0005 1.0011 1.6156 2.2746 2.8614 3.3359 3.6701 4.1219 7.7332 7.8583 8.2835 9.5686 10.848 12.0736 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 1.0012 1.0004 1.0001 1.0001 1.0017 0.9994 0.9991 1.0002 1.0004 0.9988 1.0002 1.0002 0.9995 0.9998 u2 1.0012 1.0025 0.9995 0.9931 0.9949 0.9978 0.9973 0.9989 0.9993 0.9997 1.0165 1.1141 2.1397 2.7888 u3 1.0002 1.0027 0.9992 0.9935 0.9925 0.9974 0.9973 1 0.9997 1.0012 1.0173 1.1147 2.1405 2.7905 u4 0.9684 0.9816 1.0059 1.0493 1.182 1.5796 2.455 2.8426 2.9714 3.0025 3.0148 3.08 4.1242 4.7995 u5 0.9695 0.9821 1.006 1.0522 1.1824 1.5808 2.4551 2.8429 2.9714 3.0028 3.0143 3.0802 4.124 4.8013 u6 0.9697 0.9806 1.0066 1.0576 1.1891 1.5819 2.4541 2.8411 2.9706 3.0134 3.0663 3.3089 5.4109 6.6532 u7 0.9688 0.9802 1.0065 1.0566 1.188 1.5815 2.4543 2.8404 2.9705 3.0122 3.0667 3.3087 5.4124 6.6551 u8 2.7742 2.898 2.9707 3.0198 3.1266 3.5406 4.4866 4.9057 5.0421 5.061 5.0494 5.1723 7.3692 8.7048 u9 2.7759 2.8996 2.9696 3.016 3.1241 3.5415 4.4867 4.9067 5.0432 5.0601 5.0501 5.1727 7.3707 8.706 u10 2.7715 2.9072 2.9916 3.0457 3.1402 3.541 4.4834 4.9035 5.0525 5.1122 5.2228 5.6928 8.9013 10.681 u11 2.77 2.9062 2.9926 3.0494 3.1422 3.5425 4.4833 4.9039 5.0525 5.1118 5.2217 5.6928 8.9024 10.6801 u12 2.8379 3.0216 3.1657 3.3215 3.6581 4.5549 6.2418 6.9491 7.1699 7.1725 7.1285 7.4272 10.8677 12.8191 u13 2.8393 3.0233 3.1642 3.3159 3.6531 4.5542 6.2414 6.9493 7.1687 7.1707 7.1292 7.4281 10.8681 12.8187 u14 2.844 3.017 3.1421 3.2814 3.6249 4.5445 6.2417 6.9759 7.25 7.3803 7.6122 8.4242 12.6721 14.9756 u15 2.843 3.0158 3.1438 3.2861 3.6295 4.5453 6.2415 6.9762 7.2509 7.3814 7.6109 8.4241 12.6723 14.9747 u16 4.911 5.0847 5.2173 5.3247 5.5906 6.5342 8.4252 9.2104 9.4291 9.3921 9.4171 10.0811 14.7326 17.2923 u17 4.8946 5.078 5.2225 5.3361 5.5964 6.5309 8.4176 9.2059 9.4328 9.3936 9.4161 10.0799 14.7331 17.2755 u18 4.8828 5.032 5.1525 5.263 5.5632 6.5493 8.4939 9.3909 9.7733 10.0241 10.4656 11.538 16.821 19.7523 u19 4.8993 5.0389 5.1478 5.2534 5.5595 6.5509 8.5005 9.3955 9.768 10.0192 10.4628 11.5406 16.8423 19.666 u20 5.4537 5.6751 5.8353 6.0525 6.7077 8.1966 10.6339 11.6235 11.9277 11.9919 12.2335 13.2526 19.0855 22.4952 u21 5.4274 5.661 5.8447 6.0828 6.7436 8.2344 10.6663 11.6306 11.9181 11.9835 12.2406 13.2955 19.2025 22.1794 u22 5.4211 5.7314 5.9947 6.2932 6.9708 8.5154 11.1197 12.3574 12.9096 13.3504 13.8605 15.0255 21.46 25.7242 u23 5.446 5.7457 5.9865 6.2653 6.934 8.4705 11.0711 12.3354 12.9262 13.3985 13.9572 15.2319 21.8968 24.8484 u24 7.601 7.9092 8.1116 8.2986 8.8843 10.5567 13.4789 14.6975 15.1159 15.345 15.7488 16.9733 24.1121 29.7447 u25 7.6905 7.9139 8.0671 8.234 8.8098 10.4713 13.4082 14.7119 15.2287 15.5598 16.121 17.6005 25.2362 28.0103 u26 8.0227 8.3661 8.5885 8.7912 9.4292 11.2659 14.6004 16.3761 17.081 17.4332 17.9118 19.3511 27.4658 34.5679 u27 7.8908 8.3208 8.642 8.9175 9.6219 11.5386 14.97 16.8358 17.7127 18.2141 18.9411 20.7343 29.5377 32.086 u28 9.4399 10.0496 10.4616 10.7875 11.5373 13.6107 17.3205 19.1194 19.8684 20.2666 20.8688 22.6464 32.0788 40.6327 u29 9.7624 10.4834 10.962 11.3065 12.0909 14.2876 18.2519 20.3764 21.561 22.2111 22.9314 24.8269 35.0018 37.4081 u30 10.8696 11.8503 12.6479 13.2236 14.1807 16.6639 21.0844 23.2372 24.2835 24.8299 25.4818 27.4224 38.4187 45.0872 u31 13.0935 14.0851 14.9452 15.6218 16.7225 19.5472 24.5629 26.8501 27.8003 28.1675 28.6568 30.5887 42.5428 49.499 SNR 28 29 30 31 32 33 34 35 36 37 38 39 40 u1 0.9976 0.9987 1.0014 1.025 2.4413 2.8939 2.9843 2.9997 3.0019 3.0007 3.0007 3.0003 2.9995 u2 2.9488 2.9915 3.0025 3.018 4.4383 4.8976 4.9895 5.0043 5.0061 5.0036 5.003 5.0018 5.001 u3 2.9479 2.9924 3.0037 3.0632 5.9167 6.8058 6.9842 7.0135 7.0137 7.0097 7.0074 7.0054 7.0045 u4 4.9619 5.0094 5.0187 5.0331 7.9068 8.8211 9.0048 9.0324 9.0288 9.0203 9.0152 9.0116 9.0111 u5 4.9639 5.011 5.0222 5.1327 9.4519 10.7571 11.0224 11.0604 11.0525 11.0369 11.0279 11.0206 11.0185 u6 6.9622 7.042 7.0521 7.0424 11.4366 12.7933 13.0677 13.1031 13.086 13.0608 13.0457 13.0341 13.0292 u7 6.9646 7.0451 7.0661 7.2657 13.0678 14.7709 15.1192 15.1604 15.1306 15.0937 15.0694 15.0521 15.0437 u8 9.0372 9.1166 9.1087 9.0645 15.0544 16.8389 17.2032 17.2373 17.1893 17.1369 17.1017 17.0762 17.0621 u9 9.0366 9.12 9.1529 9.5267 16.783 18.8721 19.3026 19.3344 19.2643 19.1918 19.1426 19.1063 19.0849 u10 11.1331 11.2301 11.1846 11.1868 18.7849 20.9854 21.4382 21.4555 21.3571 21.2603 21.194 21.1446 21.1144 u11 11.1295 11.2429 11.3066 11.9962 20.6177 23.0888 23.5996 23.6025 23.4702 23.3435 23.2559 23.1917 23.1505 u12 13.3129 13.3994 13.2789 13.5349 22.654 25.265 25.8011 25.7794 25.6052 25.4431 25.3306 25.2483 25.1935 u13 13.316 13.4449 13.5855 14.661 24.5975 27.4555 28.0387 27.9889 27.7649 27.5612 27.4193 27.3164 27.2455 u14 15.5542 15.6103 15.4321 16.1384 26.6918 29.7155 30.3242 30.2341 29.9519 29.6994 29.5231 29.3957 29.3073 u15 15.58 15.7567 16.0956 17.4614 28.7572 32.0137 32.6572 32.518 32.1673 31.8602 31.6441 31.4885 31.3787 u16 17.887 17.8671 17.8082 18.9525 30.94 34.3846 35.0455 34.8442 34.4149 34.0451 33.7833 33.5958 33.4606 u17 17.9845 18.2619 18.9235 20.4071 33.1458 36.8156 37.4911 37.2161 36.6987 36.2565 35.9437 35.7192 35.5554 u18 20.2884 20.2456 20.5488 21.964 35.4548 39.3279 40.0014 39.6382 39.0206 38.4973 38.1256 37.8593 37.6646 u19 20.6026 21.1199 21.993 23.5441 37.8295 41.9212 42.5806 42.1143 41.383 40.7696 40.3329 40.0202 39.7891 u20 22.8105 22.9898 23.6434 25.2095 40.3124 44.6095 45.2363 44.6495 43.79 43.0773 42.5661 42.2016 41.9315 u21 23.6105 24.4211 25.3021 26.9381 42.8978 47.3978 47.9743 47.2486 46.2474 45.4239 44.8319 44.407 44.0928 u22 25.7141 26.2598 27.0831 28.76 45.609 50.2974 50.8009 49.9168 48.7598 47.8129 47.1293 46.6391 46.2746 u23 27.2209 28.0726 28.951 30.6768 48.453 53.3172 53.7241 52.6624 51.3323 50.249 49.4658 48.9001 48.4795 u24 29.302 30.0719 30.9486 32.7041 51.4455 56.4693 56.7544 55.4931 53.9725 52.7382 51.8433 51.1958 50.7105 u25 31.3751 32.209 33.0801 34.8521 54.6007 59.7663 59.9029 58.419 56.6876 55.2875 54.2702 53.5266 52.974 u26 33.7153 34.532 35.3703 37.136 57.9366 63.2251 63.1856 61.4525 59.489 57.9066 56.7507 55.9047 55.2723 u27 36.2816 37.0684 37.8335 39.572 61.4759 66.868 66.6219 64.6108 62.39 60.607 59.2976 58.3332 57.6109 u28 39.1419 39.8412 40.4977 42.1824 65.2512 70.7275 70.2394 67.918 65.413 63.4057 61.9235 60.8256 60.0019 u29 42.336 42.8943 43.4022 45.0041 69.3127 74.8524 74.0829 71.4105 68.5885 66.3283 64.6487 63.4014 62.4582 u30 45.9471 46.3002 46.6146 48.1025 73.7506 79.3277 78.2264 75.1519 71.9717 69.4194 67.5124 66.0884 65.0072 u31 50.1806 50.2503 50.2989 51.6274 78.7737 84.3532 82.8441 79.2912 75.6839 72.7834 70.6068 68.9588 67.7069

e4) 4096-QAM/64-PAM for a Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9963 0.9978 1.0042 1.0018 0.9993 1.0199 1.0097 1.0072 1.0028 0.9994 0.9999 0.9996 1.0002 1.0005 u2 0.9888 0.995 1.0058 1.0009 1 1.0401 1.0467 1.0288 1.0323 1.0103 1.0036 0.9995 1 1.0007 u3 0.9918 0.9943 1.0101 1.0036 1.0003 1.0198 1.0337 1.018 1.0303 1.0099 1.0047 0.9997 1.0001 1.0009 u4 0.9541 0.9962 0.9955 0.9907 1.0023 1.0376 1.0885 1.0841 1.0665 1.0416 1.0207 1.0048 0.9958 0.9914 u5 0.9509 0.9947 0.9963 0.9911 1.0019 1.0575 1.1007 1.0947 1.0687 1.0415 1.0205 1.0045 0.9959 0.9919 u6 0.9572 0.994 1.0008 0.9947 1.0008 1.0371 1.0611 1.0713 1.0375 1.0295 1.018 1.0044 0.9963 0.9921 u7 0.9601 0.9933 1.0043 0.998 0.9999 1.0167 1.049 1.061 1.0352 1.0293 1.0191 1.0045 0.9965 0.9922 u8 0.8508 0.9904 1.0057 0.9981 1.0011 1.0359 1.1057 1.2062 1.3196 1.4848 1.7124 1.9789 2.2284 2.4296 u9 0.8497 0.9921 1.0036 0.9975 1.0009 1.0568 1.1177 1.2173 1.323 1.4854 1.7111 1.9774 2.229 2.4304 u10 0.8453 0.9927 0.9998 0.9957 1.0008 1.0777 1.1579 1.2437 1.3637 1.5033 1.7169 1.977 2.2279 2.4297 u11 0.8497 0.9966 0.9966 0.9945 1.0008 1.0584 1.1449 1.2318 1.3601 1.5036 1.7176 1.9772 2.2285 2.4298 u12 0.8794 0.9961 1.0066 1.0036 0.9997 1.04 1.0892 1.1572 1.3143 1.456 1.6837 1.9674 2.2398 2.4752 u13 0.8775 0.9967 1.0043 1.0016 1 1.0598 1.1014 1.1687 1.3174 1.4567 1.6825 1.9661 2.2404 2.4761 u14 0.8838 0.9993 1.0044 1.0026 0.9999 1.0395 1.0619 1.144 1.2769 1.4404 1.6764 1.9651 2.2423 2.4776 u15 0.887 1.0004 1.0046 1.0026 1.0005 1.0192 1.05 1.1336 1.2731 1.4409 1.6771 1.9652 2.2428 2.4777 u16 1.3685 2.044 2.4233 2.7677 2.9386 3.5023 3.4408 3.2474 3.2673 3.4167 3.6611 3.9531 4.2293 4.4538 u17 1.3632 2.0409 2.4206 2.7543 2.926 3.031 3.3601 3.2589 3.2953 3.4403 3.6759 3.9601 4.2313 4.4531 u18 1.3522 2.036 2.4072 2.7164 2.8659 2.7928 3.1046 3.2433 3.3198 3.4991 3.737 4.0075 4.2628 4.4661 u19 1.3584 2.0387 2.4131 2.7296 2.876 3.0328 3.1327 3.2291 3.2928 3.4736 3.7215 3.9997 4.2609 4.4673 u20 1.2937 2.0217 2.3696 2.6067 2.872 2.7985 2.8894 3.0788 3.3078 3.5536 3.8874 4.2677 4.632 4.955 u21 1.2893 2.0179 2.3654 2.5953 2.8622 2.6481 2.879 3.0908 3.3328 3.5791 3.9074 4.2792 4.6369 4.954 u22 1.3005 2.0217 2.3804 2.6264 2.9212 2.7978 2.9999 3.0955 3.3114 3.5221 3.8387 4.2143 4.5858 4.9287 u23 1.3059 2.0243 2.3849 2.6377 2.9333 3.0347 3.0216 3.0827 3.286 3.4971 3.8215 4.2031 4.5824 4.9304 u24 1.536 2.0277 2.3595 2.6209 2.931 3.5055 3.4745 3.7641 4.5388 4.8012 5.2768 5.7983 6.2845 6.6904 u25 1.5286 2.0274 2.3608 2.611 2.9209 3.0294 3.3939 3.7415 4.5688 4.8766 5.3692 5.8801 6.3465 6.73 u26 1.5142 2.0263 2.351 2.5814 2.8639 2.7958 3.1184 3.6371 4.2838 4.7955 5.3854 5.9967 6.555 7.028 u27 1.5207 2.0302 2.3596 2.5937 2.8759 3.0301 3.1528 3.6471 4.2441 4.7386 5.3092 5.9145 6.4785 6.9667 u28 1.6081 2.0374 2.397 2.7137 2.8798 3.4906 3.7542 4.4918 4.6545 5.4141 6.1357 6.9502 7.6934 8.3177 u29 1.5999 2.0376 2.3962 2.7007 2.8677 3.0254 3.6131 4.3043 4.6739 5.427 6.2138 7.0723 7.8706 8.5561 u30 1.6138 2.0443 2.4108 2.7391 2.9274 3.4965 4.488 4.9563 5.6429 6.2434 7.0601 7.9787 8.901 9.7418 u31 1.6203 2.0495 2.4173 2.752 2.9369 5.0575 5.6783 6.2681 6.9732 7.6928 8.5941 9.597 10.5869 11.4949 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 1.0004 1.0002 1.0002 0.9998 0.999 0.9988 0.9995 0.9999 1.0013 0.9999 1.001 0.9997 1.0009 0.9992 u2 1.0009 0.9991 0.9984 0.9984 1.0001 0.9996 0.9992 1.0004 1.0032 1.0364 1.3959 1.9271 2.272 2.494 u3 1.0008 0.9992 0.9986 0.9983 0.9997 0.998 0.9988 1.0013 1.0018 1.037 1.3944 1.9264 2.2732 2.4945 u4 0.9953 1.0125 1.067 1.2356 1.6294 2.0374 2.3337 2.5341 2.6647 2.7604 3.1499 3.7388 4.1332 4.3943 u5 0.9956 1.0127 1.067 1.2354 1.6298 2.0374 2.3334 2.5347 2.6639 2.7604 3.1496 3.7379 4.1327 4.3952 u6 0.9956 1.0133 1.0683 1.2372 1.6304 2.0374 2.3318 2.5328 2.6769 2.8536 3.6527 4.7448 5.4651 5.9409 u7 0.9957 1.0135 1.0683 1.2366 1.6304 2.0366 2.3321 2.5362 2.6761 2.8534 3.6538 4.7432 5.4655 5.9407 u8 2.5769 2.6774 2.7777 2.9864 3.4541 3.93 4.2773 4.5077 4.6411 4.7342 5.5345 6.7158 7.4777 7.9756 u9 2.5774 2.6773 2.7771 2.9867 3.4539 3.931 4.2766 4.5089 4.6405 4.7345 5.5352 6.7145 7.478 7.9745 u10 2.5794 2.6833 2.784 2.9906 3.4555 3.9297 4.2772 4.5202 4.7063 5.0028 6.2647 7.8812 8.9382 9.6301 u11 2.5793 2.6837 2.7837 2.9912 3.4561 3.9294 4.2768 4.5204 4.7061 5.0025 6.2637 7.8827 8.9384 9.6296 u12 2.6756 2.8656 3.1097 3.5858 4.4555 5.277 5.8584 6.2318 6.4228 6.6184 7.9618 9.7611 10.9166 11.6754 u13 2.6764 2.8653 3.1091 3.5859 4.4552 5.2757 5.8595 6.2314 6.4225 6.6189 7.9616 9.7632 10.9185 11.6664 u14 2.6747 2.8576 3.1006 3.577 4.4507 5.2792 5.8832 6.3219 6.6852 7.215 8.9989 11.1777 12.5855 13.5279 u15 2.6746 2.8581 3.1004 3.5775 4.4509 5.2795 5.8851 6.3212 6.6842 7.2149 8.9993 11.1786 12.5908 13.4849 u16 4.6252 4.7674 4.9751 5.474 6.4759 7.4011 8.0147 8.3718 8.5777 8.9581 10.8873 13.2883 14.7944 15.8428 u17 4.6243 4.7676 4.9767 5.4757 6.4751 7.3997 8.0136 8.372 8.5775 8.9585 10.885 13.2918 14.8184 15.6955 u18 4.6188 4.7505 4.9585 5.4675 6.4921 7.4646 8.1858 8.7429 9.2532 9.94 12.2345 14.9831 16.6805 18.0725 u19 4.62 4.7491 4.9578 5.4681 6.4921 7.4665 8.1853 8.7398 9.2525 9.9394 12.2364 15.0095 16.8025 17.6716 u20 5.246 5.5472 5.9566 6.7028 8.0145 9.1828 9.9708 10.5001 10.9359 11.5978 14.1236 17.1287 18.9131 20.8359 u21 5.2441 5.5486 5.9602 6.7104 8.0232 9.1919 9.9745 10.4999 10.9341 11.6041 14.1646 17.2749 19.325 20.0208 u22 5.2556 5.6032 6.0637 6.8816 8.3055 9.641 10.6757 11.4966 12.1712 12.9965 15.8137 19.1281 21.168 23.862 u23 5.2584 5.602 6.0592 6.8738 8.2927 9.6278 10.6671 11.5018 12.202 13.088 16.0518 19.6555 22.0945 22.6034 u24 7.0279 7.3462 7.7844 8.6613 10.2586 11.7039 12.7329 13.483 14.0789 14.878 17.9826 21.7256 24.1425 27.5194 u25 7.0459 7.3437 7.7662 8.6344 10.2325 11.6913 12.7532 13.5672 14.2758 15.2586 18.6869 22.8323 25.575 25.8754 u26 7.4305 7.8203 8.3639 9.4101 11.2613 12.9619 14.2091 15.1187 15.8369 16.8096 20.4248 24.7955 27.6541 31.8142 u27 7.3941 7.8194 8.4057 9.5027 11.4236 13.2128 14.5744 15.6519 16.6054 17.8237 21.8049 26.5569 29.6567 29.6686 u28 8.8516 9.3478 9.9831 11.1654 13.2585 15.161 16.5544 17.6098 18.5 19.6965 23.9472 29.0147 32.2679 37.1329 u29 9.1461 9.7003 10.4171 11.7322 14.0437 16.204 17.8423 19.1046 20.1574 21.4926 26.1156 31.5831 35.0526 34.4897 u30 10.4828 11.1807 12.0295 13.5243 16.1109 18.4804 20.2275 21.5413 22.6144 23.9997 29.0224 34.929 38.6023 41.5575 u31 12.3176 13.1061 14.0796 15.7967 18.7604 21.4433 23.3683 24.7641 25.8663 27.2995 32.8238 39.2987 43.2007 45.9849 SNR 28 29 30 31 32 33 34 35 36 37 38 39 40 u1 1.0006 1.0043 1.4608 2.031 2.3634 2.5782 2.7135 2.8007 2.8562 2.8925 2.9145 2.932 2.9432 u2 2.6454 2.7379 3.2219 3.8448 4.2255 4.4775 4.6426 4.7502 4.8197 4.8656 4.8927 4.9155 4.9282 u3 2.6449 2.746 3.6983 4.8763 5.5926 6.0595 6.3617 6.5573 6.6818 6.7624 6.8134 6.8524 6.8778 u4 4.5762 4.6828 5.6197 6.8402 7.5722 8.051 8.3598 8.5611 8.6878 8.7697 8.8219 8.8609 8.8865 u5 4.5757 4.7079 6.1651 7.912 8.9681 9.6583 10.0999 10.3859 10.5661 10.6838 10.7566 10.8106 10.8472 u6 6.2598 6.4365 7.8821 9.7373 10.8558 11.5914 12.0627 12.3691 12.5612 12.6874 12.763 12.8207 12.8615 u7 6.2627 6.5065 8.5398 10.8859 12.31 13.2454 13.8413 14.2281 14.47 14.6273 14.7205 14.7934 14.8444 u8 8.3042 8.4445 10.4315 12.8891 14.3481 15.3017 15.9032 16.2913 16.5325 16.6862 16.7743 16.8469 16.8975 u9 8.3131 8.6065 11.2028 14.1091 15.8609 17.0043 17.7263 18.1889 18.4766 18.6587 18.7627 18.8479 18.907 u10 10.0729 10.254 12.8833 15.9704 17.8101 19.0084 19.7625 20.244 20.5396 20.7276 20.8283 20.9151 20.9752 u11 10.1062 10.5627 13.7734 17.2797 19.3987 20.7764 21.6431 22.1941 22.5302 22.7431 22.8571 22.9529 23.0199 u12 12.1078 12.3025 15.599 19.2948 21.4876 22.9043 23.7857 24.3407 24.6737 24.8824 24.9883 25.0776 25.1403 u13 12.2211 12.8281 16.6269 20.7185 23.1709 24.7554 25.7402 26.3568 26.7257 26.9539 27.0702 27.1641 27.23 u14 13.9787 14.3539 18.3392 22.6727 25.2367 26.8878 27.9051 28.5338 28.9056 29.1316 29.2408 29.3276 29.3905 u15 14.2723 15.1126 19.5353 24.2439 27.0471 28.8505 29.9595 30.6383 31.0373 31.2752 31.3895 31.4767 31.5389 u16 16.1851 16.7817 21.4333 26.3916 29.2986 31.147 32.2702 32.9453 33.3306 33.5558 33.6536 33.727 33.7773 u17 16.7562 17.7277 22.7796 28.1062 31.2381 33.2292 34.4336 35.1516 35.5544 35.7864 35.8824 35.9518 35.997 u18 18.3851 19.2664 24.6112 30.2335 33.5042 35.5666 36.7993 37.5228 37.9155 38.1359 38.2116 38.2677 38.2999 u19 19.2499 20.3968 26.1323 32.1242 35.6097 37.8022 39.1019 39.8565 40.2573 40.4733 40.5406 40.5882 40.6091 u20 21.0165 22.1002 28.1574 34.4644 38.0874 40.3385 41.6513 42.3946 42.7722 42.9647 43.0011 43.0265 43.0262 u21 22.1679 23.4306 29.8838 36.5679 40.3963 42.7627 44.1297 44.8896 45.2621 45.4415 45.4589 45.4682 45.4529 u22 23.9006 25.1704 31.9904 39.027 43.0119 45.4482 46.8305 47.576 47.92 48.069 48.0512 48.0322 47.99 u23 25.3642 26.7556 33.9846 41.4123 45.5943 48.1289 49.5435 50.2892 50.6125 50.7335 50.6844 50.639 50.5714 u24 27.3645 28.7536 36.3885 44.2002 48.5385 51.1272 52.5353 53.2485 53.5222 53.5931 53.4946 53.4105 53.3077 u25 29.1484 30.6214 38.698 46.9287 51.4594 54.1327 55.5551 56.2467 56.4806 56.5119 56.3625 56.2412 56.1041 u26 31.3343 32.829 41.3722 50.0315 54.734 57.4607 58.8707 59.512 59.683 59.6552 59.4393 59.268 59.0883 u27 33.5648 35.1146 44.1486 53.2678 58.1622 60.9496 62.3471 62.9389 63.0415 62.9454 62.6599 62.439 62.2059 u28 36.2682 37.8272 47.3995 57.0085 62.0839 64.905 66.2558 66.7683 66.7757 66.5764 66.2081 65.9151 65.6227 u29 39.1974 40.7685 50.93 61.0847 66.3515 69.2122 70.5087 70.932 70.83 70.5214 70.0572 69.6802 69.3125 u30 42.8228 44.3725 55.219 65.9903 71.458 74.3362 75.5397 75.8248 75.5766 75.0956 74.5263 74.0405 73.5803 u31 47.4691 48.9596 60.6605 72.1993 77.8935 80.7711 81.8379 81.9286 81.4804 80.7898 80.0683 79.4178 78.8141

f1) 16384-QAM/128-PAM for a Non-Fading Channel

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 1 0.9993 1 0.9983 1.0007 1.0015 1.0005 1.034 0.9706 0.9792 0.9884 0.9946 1 1.0017 u2 0.9996 0.9966 0.9973 0.9973 1.0014 1.0022 1.0008 1.0677 1.0314 0.9448 0.9812 0.987 0.9986 1.0025 u3 0.9997 0.9957 0.9967 0.9982 1.0024 1.0036 1.0013 1.0365 1.0638 0.9658 0.9922 0.9931 0.9987 1.0014 u4 0.9989 0.9931 0.9864 0.991 1.0016 1.0036 1.0011 1.0667 1.1349 1.0711 0.9776 0.9939 0.9879 0.9959 u5 0.9989 0.9922 0.9863 0.9895 1.0024 1.0048 1.001 1.0998 1.0995 1.0474 0.9662 0.989 0.9878 0.9977 u6 0.9993 0.9922 0.9882 0.99 1.0037 1.0057 1.001 1.0673 1.0313 1.0874 0.973 0.9976 0.9894 0.9975 u7 0.9993 0.9916 0.9875 0.9909 1.0047 1.0072 1.001 1.0344 1.0642 1.111 0.984 1.0034 0.9894 0.9963 u8 0.9951 0.9917 0.9456 0.9589 0.9962 0.9983 1.0007 1.067 1.1363 1.2505 1.0822 1.0041 0.9777 0.9679 u9 0.9951 0.9914 0.9455 0.9577 0.9964 0.9989 1.0003 1.1002 1.1015 1.2244 1.0692 0.9982 0.9776 0.9695 u10 0.9947 0.9897 0.9433 0.9569 0.9964 0.9991 1.0003 1.1343 1.1738 1.1804 1.0619 0.9896 0.9761 0.9704 u11 0.9948 0.9893 0.9427 0.9579 0.997 0.9997 1.0005 1.1 1.2107 1.2066 1.0748 0.9955 0.9761 0.9693 u12 0.9957 0.9901 0.9516 0.9639 0.9992 1.0016 1.0001 1.0653 1.135 1.0796 1.094 0.995 0.9867 0.9751 u13 0.9956 0.9895 0.9517 0.9627 0.9995 1.0023 1.0004 1.0987 1.0997 1.0561 1.0806 0.9892 0.9865 0.9767 u14 0.996 0.9899 0.9535 0.9633 1.0005 1.0031 1.0014 1.0659 1.0325 1.0964 1.0878 0.9976 0.988 0.9764 u15 0.9961 0.9895 0.953 0.9642 1.0011 1.0037 1.0025 1.0336 1.0658 1.1205 1.1011 1.0033 0.9881 0.9754 u16 0.9984 0.9899 0.8171 0.8546 1.0039 1.0033 0.9981 1.0672 1.1362 1.2542 1.5262 1.8221 2.2124 2.5552 u17 0.998 0.9881 0.8182 0.8543 1.0029 1.003 0.9991 1.1011 1.1004 1.2266 1.5101 1.8088 2.2165 2.5557 u18 0.9973 0.9857 0.8174 0.8547 1.0021 1.0026 1.0001 1.1349 1.1725 1.1819 1.5083 1.792 2.2072 2.5533 u19 0.997 0.9839 0.8178 0.8565 1.0014 1.002 1.0005 1.1002 1.2089 1.2075 1.5252 1.8052 2.2032 2.5518 u20 0.9959 0.9826 0.8116 0.8518 0.9992 1.0015 1.0022 1.1352 1.2878 1.3476 1.5028 1.8306 2.2015 2.5399 u21 0.9954 0.9808 0.8125 0.8518 0.9982 1.0008 1.0025 1.17 1.2499 1.3196 1.4861 1.8168 2.2056 2.5406 u22 0.9955 0.9789 0.815 0.8533 0.9979 1 1.0026 1.135 1.1725 1.3648 1.4886 1.8343 2.215 2.5421 u23 0.9952 0.9769 0.8156 0.8551 0.9971 0.9994 1.0024 1.1007 1.2087 1.3912 1.5052 1.8483 2.2106 2.5402 u24 1.0005 0.9931 0.845 0.8795 1.0034 1.0026 0.9971 1.0677 1.1353 1.2436 1.3577 1.8233 2.2108 2.5682 u25 1.0003 0.9929 0.8454 0.879 1.0031 1.0023 0.9974 1.1013 1.0999 1.2172 1.3421 1.8099 2.2148 2.569 u26 0.9997 0.9917 0.844 0.8788 1.0024 1.0022 0.9976 1.1352 1.1719 1.1732 1.3371 1.7933 2.2056 2.5669 u27 0.9996 0.9914 0.8441 0.8798 1.0023 1.0022 0.9975 1.1008 1.2084 1.1991 1.3532 1.8066 2.2015 2.5654 u28 1.0004 0.9915 0.8515 0.8852 1.0043 1.003 0.997 1.0669 1.1327 1.073 1.3752 1.7831 2.2028 2.5752 u29 1.0003 0.9914 0.8517 0.8845 1.0042 1.0027 0.9971 1.1002 1.0976 1.0498 1.3592 1.7703 2.2067 2.5759 u30 1.0006 0.9923 0.8534 0.8853 1.0047 1.0027 0.9971 1.0673 1.031 1.09 1.3639 1.7861 2.2154 2.5775 u31 1.0005 0.9922 0.8533 0.8861 1.0048 1.003 0.9971 1.0348 1.0641 1.1142 1.3795 1.7986 2.2115 2.576 u32 1.001 0.9912 1.3049 1.8562 2.8726 3.3437 3.6766 4.4164 4.2323 3.9974 3.6762 3.9437 4.3434 4.6869 u33 1.001 0.9912 1.3059 1.8533 2.8736 3.3442 3.6763 4.0344 4.6857 4.1775 3.7129 3.94 4.3617 4.6707 u34 1.0007 0.9901 1.3027 1.8523 2.8709 3.3444 3.6755 3.8268 4.129 4.544 3.8489 3.9531 4.3441 4.6549 u35 1.0008 0.99 1.3027 1.8562 2.8735 3.3451 3.6754 4.0296 3.8985 4.3272 3.8033 3.9572 4.3254 4.6714 u36 1 0.9898 1.288 1.8394 2.8539 3.3416 3.6727 3.8227 3.7104 3.8963 3.8829 4.0881 4.4848 4.7175 u37 1.0001 0.99 1.2891 1.8368 2.8544 3.3419 3.6724 3.682 3.8598 4.0066 3.9374 4.088 4.5043 4.7001 u38 1.0007 0.991 1.2929 1.8392 2.8609 3.3431 3.6733 3.8219 4.1165 3.8085 3.7902 4.0676 4.519 4.7173 u39 1.0008 0.9911 1.293 1.8431 2.8632 3.3439 3.6733 4.0286 3.887 3.7183 3.7456 4.0679 4.5003 4.7354 u40 0.9961 0.9714 1.2251 1.7528 2.8145 3.3394 3.6733 3.8208 3.7067 3.5597 3.7161 4.1938 4.6751 5.1297 u41 0.9963 0.9726 1.2262 1.7507 2.8144 3.3394 3.6727 3.6829 3.86 3.6216 3.7475 4.1977 4.6923 5.1059 u42 0.9963 0.9735 1.2238 1.7496 2.8118 3.3391 3.6711 3.5697 3.7022 3.7482 3.8547 4.2244 4.6842 5.0907 u43 0.9966 0.9749 1.2239 1.7533 2.8135 3.3395 3.6709 3.681 3.5841 3.681 3.8177 4.2197 4.6663 5.1147 u44 0.9977 0.9754 1.2383 1.7696 2.8355 3.3437 3.6752 3.8266 3.7152 3.8707 3.7599 4.0885 4.4867 5.034 u45 0.998 0.977 1.2392 1.7673 2.8354 3.3437 3.6748 3.681 3.8683 3.9779 3.7926 4.0884 4.506 5.0119 u46 0.9987 0.9788 1.2429 1.7696 2.8409 3.3446 3.6759 3.8263 4.1241 3.783 3.6924 4.0692 4.5205 5.0277 u47 0.9991 0.9799 1.2432 1.7733 2.843 3.3451 3.6758 4.0358 3.8954 3.6969 3.6664 4.0694 4.502 5.0496 u48 0.9972 0.9797 1.5256 2.1641 2.8191 3.3379 3.674 4.4483 4.2332 3.9685 4.3926 5.9305 7.0157 7.1789 u49 0.997 0.9815 1.5258 2.1595 2.8191 3.3376 3.6737 4.0435 4.6652 4.1389 4.5191 6.1718 6.8164 7.2237 u50 0.9964 0.9819 1.5208 2.1572 2.8158 3.3365 3.672 3.8308 4.1164 4.5 4.6254 6.4012 7.1426 7.4095 u51 0.9964 0.9832 1.5197 2.1616 2.8177 3.3369 3.6723 4.0414 3.8933 4.2885 4.5203 6.1766 7.3723 7.3415 u52 0.9954 0.985 1.5005 2.1393 2.7992 3.3311 3.6667 3.8285 3.707 3.876 4.6675 5.8214 6.8937 7.469 u53 0.9952 0.9859 1.5008 2.135 2.7992 3.3315 3.6667 3.6836 3.8623 3.9845 4.7729 5.9508 6.7776 7.5359 u54 0.9956 0.9877 1.5048 2.1374 2.8044 3.3331 3.6686 3.8296 4.1085 3.7906 4.7206 5.7884 6.5877 7.3703 u55 0.9955 0.9883 1.5038 2.1418 2.8065 3.3336 3.669 4.0381 3.8823 3.7034 4.578 5.6671 6.6852 7.3203 u56 1.0003 0.9856 1.5986 2.2732 2.8502 3.3457 3.6758 4.4277 4.2272 4.0107 6.8098 5.9404 7.0281 8.3261 u57 1.0001 0.9875 1.5984 2.268 2.8488 3.3444 3.6743 4.0363 4.6482 4.1891 6.6195 6.1853 6.8253 8.6598 u58 0.9996 0.9889 1.5931 2.2651 2.8447 3.3415 3.6721 3.8297 4.1163 4.5614 5.7764 6.4179 7.1544 8.8641 u59 0.9995 0.9906 1.5917 2.2696 2.8451 3.3406 3.6715 4.0351 3.8897 4.3447 5.6596 6.191 7.3852 8.5998 u60 1.0002 0.9943 1.6107 2.2933 2.8616 3.3435 3.6769 4.4379 4.2418 6.2574 5.5599 7.6849 8.8055 9.6276 u61 1 0.9974 1.6105 2.288 2.86 3.3413 3.6755 4.0431 4.6809 6.1223 5.7391 7.6587 8.6932 9.9296 u62 1.0004 1.0005 1.6144 2.29 2.8621 3.3393 3.6759 4.4373 6.7937 7.0647 7.3527 8.496 11.6838 11.0046 u63 1.0003 1.0033 1.6124 2.2943 2.8617 3.3378 3.6747 8.1118 8.3013 8.3718 9.0057 10.3209 9.854 13.0332 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 1.0008 0.9999 1 1 0.9994 1.0003 0.9999 1 1.0003 1.0007 1.0007 1.0007 0.9996 1.0009 u2 1.0009 0.9999 0.9999 1.0005 1.0005 1.0006 0.9998 1.0002 1.0005 1.0011 1.0006 0.9993 1.0002 1.0011 u3 1.0001 0.9998 0.9998 1.0006 1.0005 1.0005 0.9997 0.9998 1.001 1.0015 1.0002 0.9982 1.0007 1.0003 u4 1.0001 1.0016 0.9993 0.9948 0.9943 0.999 1.0007 1.0014 1.0008 1.0007 1.0135 1.0874 1.8839 2.7462 u5 1.0009 1.0016 0.9993 0.9947 0.9939 0.9991 1.0006 1.001 1.0009 1.0009 1.0138 1.0879 1.8845 2.7474 u6 1.0007 1.0011 0.9992 0.9942 0.9924 0.9988 1.0006 1.0004 1.0003 1.0012 1.014 1.0882 1.8837 2.7463 u7 0.9998 1.001 0.9991 0.9942 0.9925 0.9987 1.0006 1.0007 1.0009 1.0005 1.0135 1.0873 1.8837 2.7459 u8 0.9689 0.9815 1.0058 1.0493 1.169 1.5305 2.4126 2.8284 2.9665 3.0033 3.0148 3.0589 3.8561 4.7555 u9 0.9697 0.9815 1.0056 1.0492 1.1687 1.5304 2.4125 2.8278 2.9664 3.0033 3.015 3.059 3.8562 4.7559 u10 0.9699 0.9817 1.0055 1.0496 1.1698 1.5307 2.4119 2.8286 2.9669 3.0036 3.0148 3.0584 3.8562 4.7561 u11 0.9691 0.9816 1.0055 1.0497 1.1699 1.5305 2.4118 2.8292 2.9669 3.0034 3.0149 3.0586 3.854 4.7547 u12 0.969 0.9797 1.0057 1.0551 1.1775 1.5327 2.4121 2.8288 2.9668 3.0111 3.0576 3.2441 4.9271 6.5695 u13 0.9697 0.9795 1.0057 1.055 1.177 1.5325 2.4116 2.8286 2.9667 3.0107 3.0577 3.2451 4.9274 6.5696 u14 0.9695 0.9791 1.0056 1.0546 1.1755 1.5323 2.412 2.8275 2.9669 3.0108 3.0577 3.2451 4.9282 6.5694 u15 0.9687 0.979 1.0055 1.0548 1.1753 1.5323 2.412 2.8271 2.9668 3.0108 3.0581 3.245 4.9282 6.5697 u16 2.7702 2.8974 2.9701 3.0217 3.1155 3.4884 4.4446 4.891 5.0389 5.064 5.0544 5.1256 6.8448 8.6152 u17 2.7733 2.8969 2.9697 3.0221 3.1156 3.4886 4.4439 4.8918 5.0381 5.0641 5.0537 5.1247 6.8437 8.6127 u18 2.7713 2.8988 2.969 3.0187 3.1129 3.4886 4.4435 4.892 5.0384 5.0647 5.0539 5.1251 6.8436 8.6136 u19 2.768 2.8987 2.9692 3.0184 3.1123 3.4889 4.4445 4.8915 5.0389 5.0642 5.0546 5.1254 6.8444 8.6151 u20 2.7659 2.9081 2.9906 3.0465 3.1292 3.4897 4.4403 4.8898 5.048 5.1086 5.2014 5.57 8.2168 10.5563 u21 2.7689 2.9078 2.9902 3.0468 3.1296 3.4901 4.4402 4.8888 5.0476 5.1085 5.2016 5.5695 8.2162 10.5568 u22 2.7708 2.9054 2.9907 3.0504 3.1321 3.49 4.4409 4.8892 5.0476 5.1089 5.2009 5.5697 8.2161 10.5567 u23 2.7676 2.9054 2.9909 3.05 3.1314 3.49 4.4408 4.8892 5.0481 5.1088 5.2021 5.5698 8.2162 10.5562 u24 2.8379 3.0215 3.1624 3.3145 3.6255 4.4521 6.1678 6.9242 7.1628 7.1826 7.1349 7.3211 10.1056 12.6823 u25 2.8408 3.0213 3.1619 3.3148 3.6262 4.4522 6.1674 6.9248 7.1627 7.1825 7.1349 7.3224 10.1062 12.6839 u26 2.8388 3.0232 3.1612 3.3105 3.6215 4.4505 6.167 6.9249 7.1626 7.181 7.1341 7.3213 10.1065 12.6838 u27 2.8358 3.0231 3.1614 3.3101 3.6205 4.4502 6.1672 6.924 7.1629 7.1809 7.1352 7.3226 10.1051 12.6818 u28 2.8379 3.0146 3.1396 3.276 3.5926 4.4391 6.1658 6.9478 7.2373 7.3699 7.5672 8.2272 11.7834 14.8109 u29 2.8408 3.0142 3.1392 3.2764 3.5931 4.4392 6.1658 6.9479 7.2365 7.3696 7.5675 8.2268 11.784 14.8118 u30 2.8427 3.012 3.1397 3.2807 3.5971 4.4406 6.1659 6.9475 7.2381 7.3713 7.5677 8.2255 11.7837 14.8121 u31 2.8398 3.0118 3.1399 3.2804 3.5959 4.4403 6.1655 6.9471 7.2382 7.3713 7.5673 8.2265 11.7838 14.8114 u32 4.905 5.0812 5.2135 5.325 5.5623 6.4222 8.3424 9.1832 9.4264 9.4043 9.3988 9.8918 13.7405 17.0945 u33 4.8974 5.0829 5.215 5.3243 5.5612 6.4225 8.3441 9.1835 9.4249 9.4037 9.3995 9.8925 13.7398 17.0938 u34 4.8874 5.076 5.2182 5.3348 5.5671 6.4201 8.338 9.1798 9.4272 9.4071 9.4006 9.891 13.7388 17.1031 u35 4.8948 5.0741 5.2166 5.3355 5.568 6.42 8.3361 9.179 9.4282 9.4051 9.4001 9.8915 13.7404 17.1045 u36 4.885 5.0286 5.1483 5.2618 5.5314 6.4329 8.4049 9.3505 9.749 9.9946 10.3826 11.2919 15.7071 19.4613 u37 4.8776 5.0303 5.1496 5.2612 5.5306 6.4335 8.4058 9.3517 9.7493 9.9944 10.383 11.2909 15.7076 19.4608 u38 4.8877 5.0366 5.1467 5.2526 5.5259 6.435 8.4118 9.3554 9.7463 9.9884 10.3801 11.2952 15.7218 19.5261 u39 4.8951 5.0349 5.1452 5.2532 5.5266 6.4346 8.4112 9.3542 9.7462 9.9877 10.3803 11.296 15.7228 19.5267 u40 5.4496 5.6707 5.8312 6.0427 6.6485 8.0446 10.5356 11.5836 11.9143 11.9816 12.1731 12.9935 17.8481 21.9597 u41 5.4265 5.6719 5.834 6.0408 6.6435 8.0389 10.529 11.5843 11.9143 11.9825 12.1733 12.9944 17.8484 21.9601 u42 5.4225 5.6558 5.8389 6.0682 6.6777 8.0758 10.564 11.594 11.9068 11.9727 12.1767 13.0275 17.9412 22.2188 u43 5.4462 5.6536 5.8354 6.0699 6.6825 8.0813 10.57 11.5945 11.9058 11.9725 12.1768 13.0261 17.9437 22.2189 u44 5.4486 5.7255 5.982 6.2744 6.9056 8.3508 10.998 12.2939 12.8674 13.2919 13.7704 14.7383 20.0927 24.5954 u45 5.4255 5.7265 5.9847 6.2728 6.9005 8.3443 10.9898 12.2904 12.8677 13.293 13.7699 14.7365 20.0925 24.596 u46 5.4293 5.7408 5.9804 6.2474 6.8661 8.3021 10.9418 12.2656 12.878 13.3338 13.851 14.9101 20.458 25.3588 u47 5.4516 5.7388 5.9771 6.2491 6.8705 8.3084 10.9501 12.2696 12.8782 13.3327 13.8513 14.9118 20.459 25.3582 u48 7.6559 7.9191 8.1097 8.2864 8.8134 10.3614 13.3436 14.6402 15.0909 15.3053 15.6604 16.6484 22.572 27.6657 u49 7.5962 7.8987 8.101 8.2903 8.8247 10.3765 13.3569 14.6387 15.0847 15.3073 15.6653 16.6516 22.5734 27.6641 u50 7.7659 7.9125 8.0678 8.2301 8.7499 10.2913 13.2832 14.6429 15.1817 15.4954 15.9904 17.2129 23.5603 29.2694 u51 7.8178 7.9342 8.0761 8.2269 8.7415 10.2787 13.2705 14.6437 15.1843 15.4947 15.9844 17.2069 23.5559 29.2779 u52 7.9905 8.3659 8.5924 8.7764 9.3449 11.0377 14.3958 16.258 17.0226 17.3789 17.8016 18.9547 25.6725 31.5778 u53 7.9568 8.3388 8.5733 8.7818 9.3685 11.0789 14.4533 16.308 17.0397 17.3723 17.7872 18.9473 25.6812 31.6373 u54 7.7652 8.2889 8.6071 8.8942 9.5447 11.3315 14.8025 16.7236 17.6318 18.1013 18.7148 20.2064 27.4993 33.8765 u55 7.8166 8.3137 8.6248 8.8899 9.5217 11.2906 14.743 16.6632 17.5973 18.1025 18.7549 20.2774 27.6486 34.1856 u56 9.5716 10.0368 10.4727 10.7927 11.475 13.4022 17.1816 19.0526 19.7879 20.1226 20.5974 21.9997 29.7286 36.4886 u57 10.5558 10.1562 10.4808 10.7507 11.4153 13.3253 17.0826 18.9593 19.7761 20.2004 20.7571 22.2698 30.256 37.411 u58 10.0469 10.511 10.9283 11.2366 11.9233 13.9203 17.8741 19.9721 21.162 21.7752 22.4108 23.9661 32.3556 39.7554 u59 9.5131 10.3449 10.8696 11.2796 12.0343 14.0983 18.1489 20.3475 21.6061 22.3479 23.0885 24.8194 33.7387 41.7463 u60 9.5784 11.5603 12.3311 12.9013 13.7996 16.085 20.5183 22.6963 23.7407 24.31 24.9759 26.6835 36.0295 44.3668 u61 10.5573 11.9943 12.7965 13.3906 14.2993 16.6522 21.2455 23.5932 24.9025 25.8342 26.7381 28.6155 38.5765 47.3857 u62 12.0078 13.117 14.0906 14.9695 16.1458 18.8287 23.9395 26.4109 27.5876 28.3405 29.1578 31.0568 41.6691 50.9452 u63 14.393 15.2684 16.2378 17.167 18.4863 21.5011 27.2192 29.8709 30.9873 31.5842 32.2501 34.1089 45.4747 55.251 SNR 28 29 30 31 32 33 34 35 36 37 38 39 40 u1 0.9979 0.9994 0.9996 1.0018 1 0.9958 1.0001 0.9984 1.0002 1.0034 2.3511 2.8929 2.9812 u2 1.0007 1 0.9994 1.0053 1.2266 2.7568 2.9441 2.9904 2.9988 3.0035 4.3493 4.8979 4.9814 u3 0.9997 0.9987 0.9994 1.0059 1.2266 2.7554 2.9418 2.9923 2.9989 3.0068 5.7136 6.7911 6.9665 u4 2.9315 2.9872 2.9987 3.0069 3.1896 4.7549 4.9513 4.996 5.0029 5.0054 7.7072 8.8002 8.9696 u5 2.9336 2.9859 2.9982 3.0076 3.189 4.7564 4.949 4.9994 5.0028 5.0111 9.0998 10.7 10.96 u6 2.9337 2.9866 2.9994 3.0181 3.5189 6.5335 6.9078 6.9976 7.0097 7.015 11.0829 12.7134 12.9713 u7 2.9334 2.9865 2.9997 3.0183 3.5182 6.5332 6.9073 6.9995 7.0099 7.0231 12.5168 14.6239 14.9709 u8 4.9479 5.0032 5.0133 5.0197 5.3804 8.5371 8.928 9.0199 9.0269 9.0321 14.4903 16.643 16.9909 u9 4.948 5.0038 5.0139 5.0214 5.3799 8.5369 8.9292 9.0199 9.0271 9.041 15.9681 18.5695 19.0023 u10 4.9469 5.0038 5.0137 5.0505 5.9287 10.3494 10.9095 11.04 11.052 11.0524 17.9366 20.5989 21.033 u11 4.9474 5.0063 5.015 5.0496 5.9277 10.3496 10.9088 11.0425 11.0518 11.0678 19.464 22.5427 23.0556 u12 6.9307 7.0326 7.045 7.0381 7.657 12.3657 12.9485 13.0857 13.0908 13.0776 21.4254 24.5855 25.1004 u13 6.9312 7.0319 7.0445 7.0398 7.6568 12.3664 12.9482 13.0868 13.0908 13.1135 22.9997 26.5489 27.1403 u14 6.9306 7.034 7.0512 7.1161 8.5075 14.2266 14.9667 15.1374 15.1424 15.1029 24.9582 28.6048 29.2023 u15 6.9308 7.0339 7.0507 7.1152 8.5081 14.2263 14.9654 15.1385 15.1432 15.1828 26.5839 30.5966 31.2639 u16 9.0002 9.1099 9.1078 9.0596 10.1193 16.2649 17.0437 17.2199 17.2122 17.1228 28.5435 32.6686 33.3472 u17 9 9.1093 9.1085 9.0594 10.1198 16.2654 17.0432 17.2194 17.2139 17.293 30.2168 34.6883 35.4328 u18 9.0014 9.1102 9.1259 9.2488 11.2407 18.1881 19.1132 19.3127 19.2996 19.1443 32.1825 36.7806 37.5374 u19 9.0008 9.1102 9.1266 9.2503 11.2404 18.19 19.1131 19.3136 19.3035 19.4856 33.9092 38.8301 39.6482 u20 11.0793 11.2291 11.1982 11.0923 12.7831 20.2619 21.2378 21.4435 21.408 21.2084 35.8821 40.9457 41.781 u21 11.0811 11.2237 11.1986 11.093 12.7828 20.264 21.2361 21.4438 21.419 21.8192 37.6595 43.0323 43.9222 u22 11.08 11.2233 11.2559 11.514 14.0803 22.2679 23.3688 23.5964 23.535 23.4078 39.6452 45.1778 46.0864 u23 11.0799 11.2286 11.2575 11.5138 14.0809 22.2665 23.3675 23.5944 23.563 24.3166 41.4777 47.3044 48.262 u24 13.254 13.3977 13.3168 13.2208 15.6096 24.3937 25.5513 25.7849 25.6784 25.8019 43.484 49.4846 50.4619 u25 13.2562 13.4214 13.3181 13.2211 15.6103 24.3918 25.5503 25.7839 25.7477 26.9208 45.3687 51.6538 52.6767 u26 13.2578 13.4225 13.4828 14.0047 17.0212 26.4894 27.7584 28.0066 27.8312 28.3524 47.3978 53.8733 54.9154 u27 13.2556 13.3979 13.4821 14.0052 17.0222 26.487 27.7589 28.0087 27.9939 29.588 49.3396 56.0924 57.1743 u28 15.5004 15.7111 15.4632 15.5855 18.577 28.6855 30.0225 30.262 29.9913 31.0147 51.3978 58.3558 59.4576 u29 15.4857 15.6237 15.4644 15.5855 18.5771 28.6848 30.0223 30.2757 30.3481 32.3241 53.3977 60.6272 61.764 u30 15.4865 15.625 15.8754 16.7318 20.086 30.8885 32.3293 32.5545 32.2059 33.7617 55.4958 62.9378 64.0976 u31 15.5004 15.7115 15.8741 16.7312 20.0864 30.8896 32.3289 32.5945 32.8891 35.1249 57.5558 65.2691 66.4551 u32 17.8171 17.905 17.7218 18.2489 21.6967 33.1813 34.694 34.878 34.6021 36.5843 59.7015 67.6399 68.843 u33 17.8798 18.1687 17.7224 18.2488 21.6967 33.1827 34.6962 34.988 35.6555 38.0015 61.8319 70.0352 71.2583 u34 17.8811 18.1688 18.5635 19.6203 23.3093 35.5155 37.1099 37.2183 37.2621 39.4949 64.0329 72.4733 73.7038 u35 17.8183 17.9043 18.5607 19.6213 23.3086 35.5157 37.1257 37.4866 38.5681 40.965 66.2391 74.9438 76.1825 u36 20.4505 20.9194 20.2864 21.1594 25.0044 37.9407 39.5858 39.5997 40.1396 42.5006 68.5084 77.4569 78.6956 u37 20.2235 20.2613 20.2866 21.1597 25.0041 37.9408 39.6421 40.1825 41.5814 44.0283 70.7985 80.0072 81.2408 u38 20.2228 20.2596 21.5865 22.686 26.7369 40.4312 42.1039 42.1382 43.1702 45.6142 73.1434 82.6023 83.8204 u39 20.4514 20.9191 21.5864 22.6865 26.7378 40.4436 42.272 43.174 44.7056 47.2067 75.5241 85.2424 86.4403 u40 22.7323 22.8862 23.2637 24.3144 28.5466 43.0066 44.6578 44.9926 46.3389 48.8473 77.964 87.9349 89.0997 u41 23.3691 24.1348 23.2623 24.3135 28.5545 43.0586 45.082 46.4069 47.959 50.5165 80.4512 90.6751 91.7963 u42 23.3697 24.133 24.8626 25.9865 30.4157 45.6368 47.3199 48.1706 49.6546 52.2317 83.0006 93.4666 94.5366 u43 22.7335 22.884 24.8623 25.9901 30.4477 45.8192 48.2111 49.8024 51.365 53.9774 85.6011 96.3129 97.3205 u44 26.8707 27.7628 26.627 27.7458 32.3527 48.3313 50.2897 51.5981 53.1407 55.7749 88.2682 99.2175 100.1494 u45 25.5392 26.0216 26.6288 27.7722 32.4627 48.8191 51.7228 53.3748 54.9521 57.6155 91.0021 102.1821 103.0246 u46 25.5384 26.0217 28.4475 29.5707 34.3386 51.1757 53.7055 55.2549 56.8268 59.5099 93.8041 105.2061 105.9496 u47 26.8739 27.7594 28.4692 29.6678 34.6571 52.2186 55.4999 57.1658 58.754 61.4529 96.6737 108.2976 108.9276 u48 28.9851 29.7601 30.3758 31.4616 36.4337 54.4329 57.5125 59.1587 60.7475 63.4556 99.6202 111.4573 111.9612 u49 30.9531 31.7887 30.4711 31.7591 37.1647 56.0941 59.5286 61.2176 62.8057 65.5158 102.6436 114.6864 115.0528 u50 30.9871 31.9024 32.379 33.4641 38.8366 58.2455 61.6737 63.3609 64.9374 67.6339 105.7482 117.9917 118.2042 u51 28.9841 29.7382 32.6972 34.1786 40.0745 60.3086 63.8886 65.5921 67.1439 69.821 108.9399 121.3788 121.419 u52 36.1367 37.333 34.5326 35.8013 41.7055 62.5724 66.2226 67.9176 69.4313 72.0776 112.2236 124.848 124.7037 u53 33.1985 33.9707 35.322 37.0377 43.2892 64.913 68.6675 70.3445 71.8036 74.4055 115.6037 128.406 128.065 u54 33.3646 34.356 37.0884 38.642 45.0343 67.4166 71.2396 72.8828 74.2672 76.8106 119.0894 132.0584 131.5042 u55 35.5643 36.3584 38.4975 40.2456 46.8714 70.0657 73.9506 75.5343 76.8264 79.2998 122.6798 135.8153 135.0306 u56 39.6646 41.0237 40.2896 42.0186 48.848 72.8931 76.8123 78.3118 79.4908 81.8779 126.395 139.6847 138.6529 u57 41.88 43.1264 42.1523 43.921 50.9695 75.9027 79.8314 81.223 82.2696 84.5537 130.2427 143.6811 142.3817 u58 44.1256 45.4315 44.2271 45.9956 53.2553 79.117 83.0274 84.2827 85.1746 87.3442 134.239 147.8142 146.2294 u59 38.3088 39.301 46.5077 48.2517 55.7201 82.5548 86.4123 87.508 88.2199 90.2591 138.4055 152.109 150.2155 u60 49.7784 50.9441 49.0319 50.7149 58.3845 86.247 90.03 90.927 91.432 93.3206 142.7773 156.5952 154.3654 u61 46.7646 48.0249 51.8299 53.4212 61.2877 90.244 93.9167 94.5792 94.8467 96.5606 147.3943 161.3181 158.7214 u62 53.972 54.8835 54.9753 56.4311 64.4959 94.6335 98.1642 98.5339 98.5319 100.0465 152.3396 166.3635 163.3522 u63 58.1359 58.7942 58.632 59.9046 68.168 99.6426 102.9507 102.9731 102.6388 103.9069 157.8042 171.9112 168.4213

f2) 16384-QAM/128-PAM for a Fading Channel

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9989 0.9988 1.0029 1.0023 1.0009 1.0079 1.0046 1.0005 1.0018 0.9971 0.9989 0.9997 0.9991 1.0004 u2 0.9962 0.997 1.0044 1.0031 1.0013 1.022 1.0156 1.0084 1.0048 0.9951 0.9981 0.9994 0.9985 1.0006 u3 0.9967 0.9958 1.0074 1.0046 1.0013 1.0137 1.0141 1.0096 1.007 0.9954 0.9984 0.9994 0.9979 1.0007 u4 0.9871 0.994 1.0057 1.001 1.001 1.0342 1.0501 1.0275 1.0253 1.0156 1.0024 0.9997 0.9975 1.0011 u5 0.9859 0.9927 1.0082 1.0019 1.0012 1.043 1.0524 1.0268 1.0263 1.0136 1.0011 0.9995 0.9968 1.0013 u6 0.9879 0.9917 1.0111 1.0045 1.0011 1.0287 1.0435 1.0193 1.026 1.0138 1.0008 0.9994 0.9963 1.0013 u7 0.9885 0.9899 1.0138 1.0058 1.0007 1.0207 1.0415 1.0198 1.0271 1.0148 1.0013 0.9994 0.9958 1.0013 u8 0.9494 0.9964 0.9929 0.9874 1.0002 1.0412 1.0937 1.0881 1.0715 1.0391 1.0201 1.0035 0.9936 0.9926 u9 0.9484 0.9951 0.9943 0.9878 1.0002 1.0493 1.0955 1.0876 1.0708 1.038 1.0193 1.0034 0.9932 0.9928 u10 0.9462 0.9939 0.9943 0.9877 1.0002 1.0636 1.1048 1.0962 1.0722 1.0369 1.0191 1.0032 0.9925 0.993 u11 0.9468 0.993 0.9962 0.9887 1.0002 1.0553 1.1012 1.0967 1.0715 1.039 1.0198 1.0033 0.992 0.993 u12 0.9552 0.9922 1.0031 0.9949 1.0011 1.0348 1.0609 1.0737 1.049 1.0201 1.0156 1.003 0.992 0.9933 u13 0.9542 0.9914 1.0047 0.9955 1.002 1.0429 1.0633 1.0732 1.0486 1.0187 1.0147 1.0028 0.9916 0.9934 u14 0.9561 0.9905 1.0073 0.9983 1.0037 1.0285 1.0536 1.0649 1.0466 1.0202 1.0148 1.0029 0.9913 0.9934 u15 0.9567 0.9895 1.0089 0.9998 1.006 1.0203 1.0512 1.0654 1.0463 1.022 1.0154 1.0029 0.9906 0.9934 u16 0.846 0.9872 1.0079 0.9975 0.9977 1.0393 1.1037 1.2076 1.3294 1.4778 1.7101 1.97 2.2195 2.4304 u17 0.8463 0.9886 1.0064 0.9978 0.9995 1.0486 1.1082 1.2067 1.3296 1.4754 1.7087 1.9697 2.2196 2.4307 u18 0.8453 0.99 1.005 0.9969 1.0006 1.0635 1.1194 1.216 1.3325 1.4737 1.7084 1.9694 2.2194 2.4311 u19 0.8467 0.9912 1.0037 0.9969 1.002 1.0559 1.1172 1.2163 1.3322 1.4759 1.7097 1.9697 2.2194 2.4312 u20 0.8403 0.9907 1.0008 0.994 1.0037 1.0767 1.159 1.2426 1.3635 1.5026 1.7162 1.9703 2.2183 2.4312 u21 0.8405 0.9921 0.9983 0.9931 1.0041 1.0855 1.1625 1.2422 1.3635 1.5002 1.7148 1.9699 2.2184 2.4316 u22 0.8431 0.9952 0.9965 0.9933 1.0042 1.0717 1.1524 1.2323 1.3602 1.5018 1.715 1.9702 2.2188 2.4316 u23 0.845 0.9981 0.995 0.9925 1.0044 1.0641 1.1499 1.2325 1.3599 1.5041 1.7163 1.9704 2.2189 2.4316 u24 0.8746 0.9923 1.0083 1.0042 1.0029 1.0407 1.0981 1.1559 1.3074 1.4681 1.6823 1.9579 2.2343 2.4767 u25 0.8744 0.9931 1.007 1.0033 1.0027 1.0489 1.1008 1.1557 1.3067 1.4656 1.6809 1.9576 2.2343 2.4771 u26 0.873 0.9933 1.0054 1.0016 1.0022 1.063 1.1107 1.1651 1.309 1.4637 1.6806 1.9574 2.234 2.4776 u27 0.8741 0.994 1.0044 1.0011 1.0018 1.0547 1.1075 1.166 1.3077 1.4659 1.6819 1.9577 2.2339 2.4776 u28 0.8817 0.9961 1.0075 1.0052 1.0014 1.0346 1.0666 1.1419 1.2759 1.4395 1.6754 1.957 2.2354 2.4777 u29 0.8814 0.9967 1.0066 1.004 1 1.0428 1.0686 1.1419 1.2744 1.437 1.6741 1.9567 2.2355 2.478 u30 0.8834 0.9971 1.0064 1.0048 1 1.0285 1.058 1.1338 1.2704 1.4386 1.6743 1.957 2.2358 2.478 u31 0.8841 0.9972 1.006 1.0043 0.9994 1.0201 1.0547 1.1348 1.2687 1.4407 1.6756 1.9574 2.2358 2.4781 u32 1.3629 2.0409 2.4229 2.7785 3.0286 3.5525 3.452 3.2399 3.2723 3.4148 3.6596 3.9456 4.2195 4.455 u33 1.3616 2.0404 2.4238 2.7775 3.0179 3.3285 3.4601 3.2664 3.272 3.4212 3.6597 3.9438 4.2175 4.4543 u34 1.358 2.0382 2.4229 2.7662 2.9906 3.05 3.3984 3.2771 3.3022 3.4405 3.6743 3.9524 4.2191 4.4538 u35 1.3599 2.0382 2.4261 2.7681 2.9999 3.1665 3.3893 3.2497 3.3014 3.4349 3.6736 3.9535 4.2197 4.4544 u36 1.345 2.0329 2.4052 2.7142 2.9046 2.8657 3.0974 3.2393 3.3361 3.4975 3.7337 4.0015 4.2519 4.4678 u37 1.3438 2.0323 2.4051 2.713 2.8958 2.8059 3.1063 3.2614 3.3361 3.5053 3.7343 4.0001 4.2499 4.4671 u38 1.3479 2.0341 2.4101 2.7237 2.9186 2.9411 3.128 3.2458 3.3058 3.4856 3.7178 3.9905 4.2468 4.4675 u39 1.3497 2.034 2.4127 2.7252 2.9269 3.0236 3.1188 3.2208 3.3054 3.4793 3.7171 3.9919 4.2479 4.4682 u40 1.2826 2.0133 2.365 2.5997 2.6751 2.8004 2.9034 3.0715 3.3102 3.5467 3.8776 4.2522 4.6189 4.9499 u41 1.2818 2.0123 2.3637 2.5981 2.6701 2.7492 2.9078 3.0856 3.3109 3.554 3.8792 4.251 4.6171 4.9486 u42 1.2788 2.0097 2.3605 2.5883 2.6558 2.656 2.8982 3.0946 3.3356 3.5759 3.8991 4.2651 4.622 4.9478 u43 1.2804 2.0091 2.362 2.589 2.6631 2.6836 2.8851 3.0783 3.3366 3.5679 3.8974 4.2665 4.6241 4.9489 u44 1.2944 2.014 2.3852 2.6329 2.7231 2.8828 3.0342 3.0854 3.3064 3.5069 3.8306 4.204 4.5744 4.9257 u45 1.2935 2.0131 2.384 2.6311 2.7177 2.8219 3.0433 3.1019 3.3071 3.5137 3.8318 4.2028 4.5726 4.9245 u46 1.2972 2.0149 2.3879 2.6404 2.7354 2.9691 3.0594 3.0876 3.2821 3.4927 3.8137 4.1902 4.5683 4.9251 u47 1.299 2.0145 2.3898 2.6411 2.7422 3.0569 3.0508 3.0704 3.282 3.4857 3.8125 4.1918 4.5703 4.9262 u48 1.5313 2.0191 2.3561 2.6229 2.8594 3.5888 3.5261 3.7149 4.3926 4.8997 5.2665 5.7826 6.2706 6.6945 u49 1.5291 2.0206 2.3598 2.6233 2.8526 3.3576 3.5326 3.7612 4.3914 4.9813 5.3123 5.8072 6.2826 6.6978 u50 1.5241 2.0213 2.3599 2.6144 2.8323 3.0728 3.4598 3.7455 4.4316 5.0823 5.3952 5.8874 6.3481 6.7426 u51 1.5256 2.0228 2.3654 2.6171 2.8413 3.1848 3.4525 3.706 4.4301 4.9982 5.3435 5.8583 6.3349 6.7394 u52 1.507 2.0211 2.3471 2.5738 2.7683 2.8691 3.1305 3.6125 4.2759 4.7815 5.3532 5.9582 6.5204 7.0147 u53 1.5051 2.0226 2.3509 2.5745 2.7619 2.8099 3.1398 3.6443 4.2761 4.8302 5.3948 5.988 6.5386 7.022 u54 1.5094 2.0257 2.3572 2.5845 2.7819 2.9556 3.1622 3.6488 4.2348 4.7643 5.327 5.9103 6.4612 6.9572 u55 1.511 2.0274 2.3625 2.5872 2.7902 3.0453 3.1527 3.6138 4.234 4.7176 5.2885 5.8843 6.4457 6.9515 u56 1.6021 2.0284 2.3939 2.7143 3.1057 3.5076 3.689 4.5134 4.8429 5.1235 6.0822 6.8988 7.6405 8.2935 u57 1.5995 2.0305 2.3955 2.7123 3.0929 3.3048 3.6869 4.5115 4.842 5.2273 6.214 7.0241 7.7438 8.3667 u58 1.5941 2.031 2.3942 2.7005 3.0605 3.0374 3.5882 4.3291 4.8102 5.309 6.2458 7.0937 7.8834 8.5802 u59 1.5954 2.0347 2.3975 2.7015 3.0727 3.1457 3.5857 4.3044 4.8112 5.2174 6.1432 6.9892 7.7827 8.4912 u60 1.6145 2.0398 2.417 2.7561 3.212 3.8643 4.617 4.9699 5.625 6.2727 6.9795 7.8126 8.6889 9.531 u61 1.6118 2.0429 2.417 2.7528 3.1958 3.5371 4.4599 4.9035 5.6215 6.2593 7.0494 7.9583 8.8773 9.7608 u62 1.6162 2.0472 2.4211 2.7624 3.2323 4.2147 5.1263 5.6564 6.9712 7.0092 7.8747 8.854 9.824 10.7896 u63 1.6177 2.0493 2.4237 2.7617 3.244 5.598 6.2209 6.8304 6.9863 8.3585 9.343 10.4137 11.462 12.4776 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 0.9999 0.9999 1 1.0001 0.9997 0.9998 1.0001 0.9997 1.0005 1.0006 1.0001 1.001 1.0002 0.9999 u2 0.9999 1 1.0003 1.0003 0.9996 0.9995 0.9999 1.0002 0.9999 1.0007 1.0001 1 1.0001 1.0007 u3 0.9998 0.9998 1.0002 1.0003 0.9994 0.9993 0.9999 0.9999 1.0004 1.0009 1.0007 1.0014 1.0007 0.999 u4 0.9996 0.9978 0.9975 0.9985 0.9999 1.0003 0.9999 1.0004 1.0014 1.0275 1.3247 1.8719 2.2327 2.4633 u5 0.9996 0.9977 0.9974 0.9986 0.9997 1.0001 1.0002 0.9996 1.0019 1.0279 1.3238 1.8728 2.2336 2.4642 u6 0.9994 0.9974 0.9971 0.9984 0.9995 0.9999 0.9997 1.0005 1.0015 1.0275 1.3243 1.8711 2.2327 2.4657 u7 0.9994 0.9972 0.997 0.9984 0.9993 0.9996 1 1 1.002 1.0279 1.3238 1.8723 2.2333 2.4652 u8 0.9951 1.0119 1.0641 1.2256 1.6094 2.0167 2.3187 2.5221 2.6542 2.7457 3.0728 3.6797 4.0893 4.358 u9 0.9952 1.0118 1.0641 1.2257 1.6092 2.0163 2.3185 2.5221 2.6545 2.7465 3.0724 3.6786 4.0902 4.3579 u10 0.9953 1.0119 1.0643 1.2259 1.6091 2.0163 2.3187 2.5218 2.6545 2.7465 3.0727 3.6794 4.0906 4.3587 u11 0.9952 1.0117 1.0642 1.2259 1.6089 2.016 2.3188 2.522 2.6546 2.7466 3.0727 3.6793 4.0898 4.3588 u12 0.9945 1.0132 1.0667 1.2274 1.6105 2.0168 2.3179 2.5218 2.6643 2.8236 3.5071 4.6309 5.3838 5.8735 u13 0.9946 1.0131 1.0667 1.2275 1.6103 2.0166 2.3178 2.5218 2.6648 2.8242 3.5073 4.6315 5.3844 5.8717 u14 0.9944 1.0128 1.0664 1.2273 1.6101 2.0164 2.3178 2.5221 2.664 2.8237 3.5056 4.6308 5.3849 5.8724 u15 0.9943 1.0126 1.0663 1.2273 1.6098 2.0159 2.3178 2.5224 2.6648 2.8234 3.507 4.6313 5.3852 5.872 u16 2.5761 2.6771 2.7747 2.9747 3.4295 3.9068 4.259 4.4941 4.631 4.7146 5.3762 6.5959 7.3934 7.901 u17 2.5759 2.6769 2.7747 2.9748 3.4293 3.9071 4.2591 4.4942 4.6316 4.7147 5.3781 6.5955 7.3896 7.9034 u18 2.5761 2.6766 2.7745 2.9749 3.4291 3.9064 4.2591 4.4944 4.632 4.7157 5.376 6.5969 7.3914 7.9033 u19 2.5758 2.6765 2.7744 2.9748 3.4289 3.9064 4.259 4.4945 4.6321 4.7156 5.3768 6.5951 7.3914 7.9016 u20 2.5757 2.6807 2.7808 2.9792 3.4318 3.9075 4.2591 4.5035 4.6889 4.9481 6.0434 7.7141 8.8142 9.5277 u21 2.5756 2.6805 2.7808 2.9793 3.4316 3.9074 4.2594 4.5036 4.689 4.9489 6.0427 7.7138 8.8145 9.5234 u22 2.5753 2.6804 2.7809 2.9792 3.4314 3.9067 4.2591 4.5037 4.6881 4.9482 6.0423 7.7129 8.8163 9.5246 u23 2.5751 2.6803 2.7808 2.9792 3.4313 3.907 4.2598 4.5039 4.6882 4.9477 6.0431 7.7148 8.8138 9.5258 u24 2.6708 2.8589 3.0989 3.5599 4.4098 5.2362 5.8285 6.2089 6.4094 6.5755 7.7134 9.5764 10.7824 11.5512 u25 2.6707 2.8587 3.0989 3.56 4.4097 5.2356 5.8281 6.2088 6.4093 6.5743 7.7142 9.5751 10.7828 11.5554 u26 2.6706 2.8584 3.0987 3.5601 4.4096 5.2357 5.8291 6.2087 6.4093 6.5769 7.7139 9.5761 10.7815 11.5581 u27 2.6704 2.8584 3.0986 3.56 4.4093 5.2354 5.8289 6.2089 6.4094 6.5748 7.7127 9.575 10.7833 11.553 u28 2.6696 2.8533 3.0899 3.5516 4.4062 5.2382 5.8505 6.2904 6.6495 7.1289 8.692 10.9478 12.4191 13.3731 u29 2.6694 2.8531 3.0899 3.5517 4.4061 5.2378 5.8507 6.2908 6.6497 7.1297 8.6912 10.9479 12.4195 13.3502 u30 2.6689 2.8531 3.0901 3.5517 4.4059 5.238 5.8508 6.2906 6.6488 7.1283 8.6933 10.9474 12.4173 13.3487 u31 2.6686 2.8531 3.0901 3.5517 4.4054 5.2375 5.8508 6.2913 6.649 7.1282 8.6913 10.9473 12.4192 13.3722 u32 4.6187 4.7607 4.9645 5.4476 6.4234 7.3577 7.984 8.3511 8.5574 8.8785 10.5402 13.0392 14.617 15.5648 u33 4.6188 4.7609 4.9647 5.4476 6.4234 7.3577 7.9838 8.3502 8.555 8.8796 10.5413 13.0406 14.6184 15.6646 u34 4.6184 4.7616 4.9658 5.4485 6.4234 7.3577 7.984 8.3507 8.5578 8.8816 10.5404 13.0391 14.6312 15.6624 u35 4.6185 4.7612 4.9656 5.4485 6.4232 7.3572 7.9842 8.3515 8.5563 8.8807 10.5401 13.0401 14.6319 15.5607 u36 4.6124 4.7447 4.9489 5.4402 6.4384 7.4182 8.1423 8.6986 9.2012 9.8304 11.8335 14.6892 16.4785 17.8395 u37 4.6127 4.745 4.9491 5.4403 6.4383 7.4183 8.1423 8.6985 9.2003 9.8301 11.8338 14.6915 16.4779 17.5206 u38 4.6133 4.7442 4.948 5.4394 6.4378 7.4179 8.1433 8.6978 9.1987 9.829 11.8352 14.7102 16.5702 17.5149 u39 4.6134 4.7438 4.9478 5.4394 6.4375 7.4173 8.1427 8.6971 9.1986 9.8298 11.8374 14.7102 16.5711 17.8348 u40 5.2325 5.5363 5.94 6.6655 7.9474 9.1302 9.9272 10.4599 10.8897 11.4804 13.678 16.8135 18.7036 19.8248 u41 5.2324 5.5368 5.94 6.6657 7.9469 9.1296 9.927 10.4602 10.8893 11.4791 13.677 16.8132 18.7045 20.5433 u42 5.2307 5.5377 5.9424 6.6722 7.9544 9.1366 9.9303 10.4585 10.8877 11.4835 13.7102 16.9334 19.0442 20.5387 u43 5.2302 5.537 5.9423 6.6721 7.9545 9.1368 9.9305 10.4598 10.8879 11.4845 13.7099 16.9333 19.0433 19.8224 u44 5.2392 5.5887 6.0408 6.8364 8.2261 9.571 10.6064 11.4263 12.1002 12.8576 15.3198 18.7743 20.9002 23.5006 u45 5.2391 5.5892 6.0408 6.8366 8.2254 9.5701 10.6058 11.4262 12.099 12.8572 15.319 18.7761 20.8992 22.3178 u46 5.2404 5.5882 6.0382 6.8289 8.2148 9.5584 10.5981 11.429 12.1242 12.9343 15.5198 19.2368 21.7361 22.32 u47 5.24 5.5876 6.0381 6.8288 8.2149 9.5584 10.5982 11.4285 12.1239 12.9344 15.5203 19.2389 21.7386 23.5021 u48 7.013 7.3345 7.7637 8.6099 10.17 11.6313 12.6654 13.4186 14.012 14.7276 17.4193 21.3014 23.7907 25.5077 u49 7.0128 7.3333 7.7635 8.6113 10.1716 11.6321 12.6649 13.4183 14.0118 14.7294 17.4205 21.3024 23.7908 27.071 u50 7.0349 7.3345 7.7495 8.5872 10.1465 11.6186 12.6808 13.4891 14.1858 15.0687 18.0525 22.3301 25.1476 27.1051 u51 7.035 7.3356 7.7497 8.5859 10.1447 11.6171 12.6806 13.4899 14.1851 15.0665 18.051 22.3288 25.1536 25.5048 u52 7.4046 7.8017 8.3336 9.3452 11.1551 12.8729 14.1217 15.0367 15.7471 16.616 19.7548 24.2571 27.1695 31.6586 u53 7.4058 7.7994 8.3323 9.3489 11.1624 12.8834 14.1317 15.0426 15.7489 16.6159 19.7531 24.2712 27.2292 29.1086 u54 7.3633 7.7915 8.3632 9.4306 11.3056 13.1108 14.4682 15.5375 16.4637 17.5688 21.022 25.8837 28.9904 29.2925 u55 7.3624 7.7933 8.3644 9.4269 11.2971 13.0972 14.4521 15.5234 16.4628 17.5857 21.0793 26.0304 29.3208 31.0453 u56 8.8065 9.3135 9.9376 11.0884 13.1378 15.0593 16.4427 17.4752 18.3209 19.3541 22.9699 28.108 31.3876 34.8066 u57 8.8474 9.3315 9.9371 11.0714 13.1081 15.0256 16.4193 17.4806 18.3726 19.4911 23.263 28.6693 32.2909 36.6067 u58 9.1327 9.6836 10.3651 11.612 13.8329 15.9587 17.5435 18.7598 19.746 20.9135 24.8649 30.5061 34.1994 38.3565 u59 9.0672 9.6447 10.3583 11.6469 13.92 16.1127 17.7783 19.0856 20.2014 21.5612 25.8244 31.8572 35.8395 33.6374 u60 10.241 10.929 11.7451 13.1656 15.6366 17.9556 19.6557 20.9527 22.03 23.3514 27.7978 34.122 38.2463 41.6053 u61 10.4994 11.228 12.0958 13.598 16.2181 18.729 20.6497 22.1512 23.4014 24.8846 29.6552 36.3897 40.7559 43.927 u62 11.6406 12.4845 13.4986 15.1983 18.1005 20.8322 22.8713 24.4239 25.6952 27.2098 32.2996 39.4812 44.0647 47.2753 u63 13.3608 14.2674 15.3815 17.2797 20.5285 23.5625 25.7938 27.4371 28.746 30.303 35.8031 43.5599 48.394 51.6747 SNR 28 29 30 u1 1 0.9941 1.0006 u2 0.9961 0.9992 1.213 u3 0.9985 1.0038 1.21 u4 2.6117 2.7108 2.9641 u5 2.6119 2.7122 2.9636 u6 2.6108 2.7177 3.2056 u7 2.6092 2.7167 3.2068 u8 4.5274 4.6511 5.1068 u9 4.5254 4.6491 5.1065 u10 4.5258 4.6621 5.4289 u11 4.5276 4.6634 5.4289 u12 6.1814 6.3913 7.1006 u13 6.1801 6.3942 7.0992 u14 6.1819 6.4253 7.5493 u15 6.181 6.4219 7.5507 u16 8.2092 8.414 9.3721 u17 8.2092 8.4115 9.3723 u18 8.2196 8.493 9.9573 u19 8.2196 8.4937 9.9568 u20 9.9591 10.2022 11.5446 u21 9.9545 10.2008 11.5437 u22 9.9731 10.3908 12.2584 u23 9.978 10.392 12.2575 u24 11.9929 12.2139 13.97 u25 11.9987 12.2143 13.9706 u26 12.0585 12.6031 14.8316 u27 12.0523 12.6008 14.8311 u28 13.85 14.1771 16.4155 u29 13.8461 14.1776 16.4152 u30 14.0343 14.8201 17.4439 u31 14.0384 14.8185 17.4452 u32 16.0188 16.526 19.1973 u33 16.0226 16.5255 19.1981 u34 16.4627 17.3853 20.3747 u35 16.4617 17.3844 20.3735 u36 18.1241 18.9258 22.0463 u37 18.1257 18.9254 22.0474 u38 18.8767 19.9861 23.3893 u39 18.8812 19.9855 23.3882 u40 20.6662 21.6869 25.2366 u41 20.6656 21.6863 25.2361 u42 21.7376 22.959 26.7625 u43 21.7386 22.9576 26.7689 u44 23.4576 24.6756 28.6507 u45 23.4597 24.6791 28.6958 u46 24.8544 26.1926 30.3706 u47 24.8569 26.2204 30.5402 u48 26.8146 28.1094 32.437 u49 26.8394 28.2358 32.8644 u50 28.4818 29.8243 34.4657 u51 28.6146 30.1978 35.2449 u52 30.4923 31.9052 36.9762 u53 30.9361 32.6793 38.1036 u54 32.5927 34.2525 39.8085 u55 33.5509 35.447 41.281 u56 35.418 37.2676 43.2674 u57 36.8325 38.8242 45.0812 u58 38.7904 40.803 47.2854 u59 40.7347 42.8248 49.5626 u60 43.2185 45.313 52.3141 u61 45.8981 48.0239 55.3102 u62 49.2922 51.3988 59.013 u63 53.675 55.7554 63.7521

g) 65536-QAM/256-PAM for a Non-Fading Channel

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9999 0.9999 0.9999 0.9998 1.0006 0.9987 1.0011 1.0061 1.0106 1.0072 0.995 1.0017 1.0001 1.0007 u2 0.9999 0.9992 0.999 0.9992 1.0011 0.9977 1.0019 1.0397 0.9828 0.9887 0.9887 0.9974 1.0003 1.002 u3 0.9999 0.9995 0.9985 0.9989 1.0021 0.9968 1.0029 1.0368 0.9737 0.9812 0.9945 0.9951 1.0003 1.0014 u4 0.9995 0.9968 0.9959 0.9973 1.0025 0.9958 1.0028 1.0735 1.0355 0.9466 0.9768 0.9874 0.9983 1.0022 u5 0.9994 0.9967 0.9957 0.9971 1.0032 0.9952 1.003 1.0783 1.0464 0.953 0.972 0.9891 0.9984 1.0029 u6 0.9994 0.9975 0.9962 0.9971 1.0038 0.9945 1.0036 1.0457 1.0772 0.9704 0.9798 0.9925 0.9984 1.0017 u7 0.9995 0.9978 0.9958 0.9968 1.0047 0.9934 1.0039 1.0406 1.0667 0.9628 0.9858 0.9903 0.9983 1.0012 u8 0.9987 0.9858 0.9859 0.9897 1.0036 0.992 1.0017 1.0742 1.1355 1.0509 0.9696 0.9935 0.9849 0.9958 u9 0.9987 0.9857 0.9858 0.9894 1.0045 0.9913 1.0016 1.0791 1.1472 1.0587 0.9647 0.9952 0.9849 0.9965 u10 0.9986 0.985 0.985 0.9889 1.0049 0.9907 1.0014 1.1129 1.1145 1.0389 0.9585 0.991 0.9848 0.9978 u11 0.9986 0.9853 0.9845 0.9887 1.0057 0.9903 1.0015 1.1076 1.103 1.0312 0.9638 0.9888 0.9847 0.9973 u12 0.999 0.9882 0.9866 0.9897 1.0068 0.9896 1.0019 1.0674 1.0358 1.0697 0.9823 0.9958 0.9867 0.9966 u13 0.9989 0.9881 0.9865 0.9895 1.0072 0.9892 1.0015 1.0723 1.0465 1.0778 0.9773 0.9977 0.9867 0.9973 u14 0.999 0.9889 0.9871 0.9896 1.0081 0.9885 1.0015 1.0395 1.077 1.0982 0.9847 1.0016 0.9866 0.9962 u15 0.999 0.9892 0.9866 0.9893 1.0086 0.9877 1.0014 1.0342 1.066 1.09 0.9902 0.9995 0.9865 0.9956 u16 0.995 0.9494 0.9447 0.9568 0.9971 0.9929 0.9987 1.0732 1.1387 1.2263 1.1006 1.0039 0.9751 0.9687 u17 0.995 0.9493 0.9447 0.9567 0.9973 0.9926 0.9983 1.0784 1.1504 1.2352 1.0939 1.006 0.9752 0.9694 u18 0.9949 0.9487 0.9438 0.9563 0.9976 0.9924 0.9979 1.1121 1.118 1.2125 1.0854 1.0018 0.9753 0.9706 u19 0.995 0.949 0.9435 0.9561 0.998 0.9922 0.9978 1.1072 1.1066 1.2033 1.0915 0.9998 0.9752 0.9701 u20 0.9946 0.9465 0.9411 0.9548 0.9978 0.9918 0.9972 1.1489 1.179 1.1598 1.0703 0.9922 0.9736 0.9708 u21 0.9945 0.9465 0.9411 0.9547 0.9982 0.9916 0.9972 1.1543 1.1911 1.1686 1.064 0.9942 0.9737 0.9716 u22 0.9945 0.9473 0.9415 0.9548 0.9985 0.9913 0.9974 1.1196 1.2251 1.1908 1.072 0.9981 0.9734 0.9705 u23 0.9946 0.9476 0.9412 0.9547 0.9989 0.9912 0.9977 1.1146 1.213 1.1819 1.0782 0.9962 0.9733 0.9701 u24 0.9954 0.9588 0.9498 0.9608 1.0009 0.9914 0.9981 1.0764 1.1374 1.0787 1.0934 0.9942 0.9849 0.9756 u25 0.9953 0.9588 0.9497 0.9606 1.0012 0.9912 0.9985 1.0815 1.1491 1.087 1.0873 0.9962 0.985 0.9763 u26 0.9953 0.9581 0.949 0.9602 1.0014 0.9909 0.9988 1.1154 1.1165 1.0667 1.0794 0.9921 0.9851 0.9776 u27 0.9953 0.9584 0.9486 0.9602 1.0017 0.9905 0.9998 1.1102 1.105 1.0589 1.0858 0.9902 0.9851 0.9771 u28 0.9957 0.9611 0.9507 0.9612 1.0026 0.9902 1.0011 1.0702 1.0378 1.0988 1.1065 0.9984 0.9872 0.9765 u29 0.9957 0.961 0.9507 0.9611 1.003 0.9898 1.0021 1.0753 1.0486 1.1074 1.1007 1.0005 0.9873 0.9773 u30 0.9957 0.9618 0.9511 0.9612 1.0033 0.9894 1.0037 1.0427 1.0792 1.1286 1.1091 1.0047 0.9873 0.9763 u31 0.9958 0.962 0.9509 0.9611 1.0037 0.989 1.0047 1.0379 1.0683 1.1208 1.1161 1.0027 0.9873 0.9758 u32 0.9988 0.8594 0.8156 0.8501 1.0099 0.9903 0.9902 1.0718 1.1384 1.2695 1.5234 1.824 2.2152 2.5559 u33 0.9985 0.8605 0.8161 0.8507 1.0092 0.9905 0.9922 1.0764 1.1499 1.279 1.5153 1.8294 2.2133 2.5567 u34 0.9983 0.8605 0.8161 0.8509 1.0083 0.9905 0.993 1.1098 1.1171 1.2566 1.5053 1.8192 2.2107 2.5577 u35 0.9982 0.8619 0.8163 0.8515 1.0075 0.991 0.9949 1.1041 1.1053 1.2477 1.5134 1.8139 2.2123 2.5568 u36 0.9976 0.8606 0.815 0.8507 1.0066 0.9907 0.9959 1.1455 1.1776 1.204 1.4899 1.7992 2.2032 2.5552 u37 0.9974 0.8613 0.8154 0.8513 1.0058 0.991 0.9977 1.1501 1.1893 1.2133 1.4817 1.8044 2.2015 2.556 u38 0.9973 0.8629 0.8165 0.8521 1.005 0.9916 0.9985 1.1145 1.223 1.2361 1.4919 1.8145 2.2039 2.5549 u39 0.9972 0.8643 0.8167 0.8524 1.0041 0.992 0.9995 1.1088 1.2107 1.2273 1.5002 1.8092 2.2055 2.554 u40 0.9961 0.8555 0.8101 0.8477 1.0028 0.9899 1.0007 1.1477 1.2899 1.3449 1.4919 1.8323 2.2051 2.5426 u41 0.9959 0.8565 0.8109 0.848 1.0018 0.9902 1.0021 1.152 1.302 1.3544 1.4835 1.8378 2.2032 2.5434 u42 0.9956 0.8573 0.8107 0.8483 1.0009 0.9905 1.0026 1.1869 1.2672 1.3311 1.473 1.8272 2.2006 2.5444 u43 0.9955 0.8585 0.8111 0.8489 0.9999 0.9912 1.0032 1.181 1.2547 1.3217 1.4813 1.8216 2.2024 2.5435 u44 0.9958 0.8616 0.8132 0.8502 0.9993 0.9919 1.0037 1.1382 1.1777 1.3674 1.5058 1.8371 2.2118 2.5449 u45 0.9955 0.8627 0.8139 0.8509 0.9986 0.9925 1.0044 1.1428 1.1895 1.3769 1.4974 1.8426 2.2099 2.5458 u46 0.9955 0.8638 0.8149 0.8515 0.9979 0.9931 1.0047 1.1081 1.2233 1.4 1.5078 1.8533 2.2127 2.5446 u47 0.9954 0.865 0.8152 0.8519 0.997 0.9937 1.0048 1.1025 1.211 1.3909 1.5163 1.8476 2.2146 2.5437 u48 1.0009 0.8931 0.8438 0.8763 1.0045 0.9965 0.9947 1.0691 1.1358 1.2388 1.353 1.8195 2.216 2.57 u49 1.0007 0.8933 0.844 0.8765 1.0042 0.9965 0.9954 1.074 1.1473 1.248 1.3454 1.8248 2.2141 2.5709 u50 1.0006 0.8933 0.8436 0.8765 1.0039 0.9966 0.9957 1.1076 1.1147 1.2255 1.3359 1.8148 2.2113 2.5719 u51 1.0006 0.894 0.8436 0.8766 1.0037 0.9968 0.9963 1.1023 1.1033 1.2165 1.3437 1.8096 2.213 2.5712 u52 1.0001 0.8923 0.842 0.8758 1.0029 0.9967 0.9965 1.1435 1.1753 1.1728 1.3205 1.7949 2.2038 2.5697 u53 0.9999 0.8927 0.8422 0.876 1.0026 0.9968 0.9971 1.1485 1.1872 1.1818 1.313 1.8001 2.2019 2.5706 u54 0.9999 0.8938 0.8428 0.8763 1.0025 0.997 0.9973 1.1136 1.2211 1.2042 1.3228 1.81 2.2044 2.5697 u55 0.9999 0.8944 0.8428 0.8764 1.0024 0.9971 0.9977 1.1084 1.209 1.1952 1.3306 1.8047 2.2061 2.5689 u56 1.0008 0.9041 0.85 0.8816 1.0045 0.9982 0.9992 1.0715 1.1336 1.0908 1.3414 1.783 2.2071 2.5793 u57 1.0007 0.9044 0.8501 0.8817 1.0043 0.9982 0.9995 1.0766 1.1453 1.0989 1.3339 1.7882 2.2051 2.5802 u58 1.0006 0.9043 0.8497 0.8816 1.0041 0.9983 0.9998 1.1103 1.1127 1.0783 1.3244 1.7789 2.2021 2.5812 u59 1.0006 0.9048 0.8496 0.8816 1.0041 0.9983 1.0004 1.1051 1.1013 1.0701 1.3319 1.7741 2.2033 2.5805 u60 1.001 0.9073 0.8513 0.8826 1.0047 0.9984 1.0011 1.0662 1.0346 1.1103 1.3549 1.7883 2.2119 2.5822 u61 1.0009 0.9075 0.8515 0.8827 1.0046 0.9983 1.0015 1.0713 1.0453 1.1186 1.3473 1.7935 2.2098 2.5831 u62 1.0009 0.9083 0.852 0.8829 1.0048 0.9983 1.0018 1.0388 1.0758 1.1395 1.3569 1.8032 2.2122 2.5822 u63 1.0009 0.9088 0.8518 0.8829 1.0049 0.9983 1.0025 1.0339 1.0648 1.1309 1.3645 1.7984 2.2138 2.5815 u64 1.0014 0.8832 1.3023 1.8457 2.8713 3.3468 3.6733 4.694 4.3631 3.9582 3.6768 3.9502 4.3585 4.6922 u65 1.0014 0.8832 1.3029 1.846 2.8725 3.3462 3.6731 4.564 4.2294 3.909 3.6877 3.9552 4.3481 4.6869 u66 1.0013 0.8828 1.3019 1.8455 2.8727 3.3444 3.6729 4.0789 4.6337 4.0402 3.7072 3.9512 4.3328 4.6741 u67 1.0014 0.8832 1.3019 1.8457 2.8743 3.3445 3.6729 4.1455 4.8023 4.1009 3.6949 3.9456 4.3415 4.6799 u68 1.001 0.8812 1.2984 1.8427 2.8709 3.3391 3.6726 3.8727 4.1949 4.4441 3.7838 3.9628 4.327 4.6633 u69 1.0009 0.8813 1.2989 1.8431 2.8724 3.3383 3.6724 3.8289 4.1122 4.3664 3.7988 3.9683 4.3171 4.6583 u70 1.001 0.882 1.3002 1.8441 2.8745 3.3396 3.6725 4.0201 3.9095 4.1929 3.7754 3.9729 4.3316 4.6713 u71 1.0011 0.8823 1.3002 1.8444 2.8764 3.3397 3.6725 4.081 3.9742 4.2618 3.7613 3.9676 4.341 4.677 u72 1.0002 0.873 1.2862 1.8278 2.8526 3.3207 3.6691 3.8523 3.7713 3.9301 3.9063 4.0959 4.5016 4.7241 u73 1.0002 0.873 1.2867 1.8282 2.8534 3.32 3.6688 3.8097 3.7277 3.8931 3.9258 4.1 4.4915 4.718 u74 1.0002 0.8724 1.2859 1.8277 2.8538 3.3184 3.6686 3.6813 3.8638 3.9879 3.9571 4.098 4.4759 4.7037 u75 1.0003 0.8726 1.2859 1.828 2.8551 3.3186 3.6687 3.7161 3.9174 4.0289 3.9361 4.0933 4.4861 4.7098 u76 1.0008 0.8748 1.2899 1.8316 2.861 3.3236 3.6696 3.9052 4.1912 3.832 3.8327 4.0706 4.5005 4.7274 u77 1.0008 0.8747 1.2903 1.8318 2.8616 3.323 3.6694 3.8574 4.1077 3.7986 3.8494 4.0752 4.4907 4.7214 u78 1.0009 0.8754 1.2917 1.8329 2.8642 3.3242 3.6695 4.0837 3.9032 3.7217 3.8238 4.0784 4.506 4.7358 u79 1.0011 0.8755 1.2918 1.8332 2.8656 3.3244 3.6696 4.1502 3.9697 3.751 3.8086 4.074 4.5159 4.742 u80 0.9959 0.8487 1.2233 1.7415 2.8108 3.2753 3.6721 3.888 3.7599 3.5872 3.7421 4.1984 4.6901 5.1385 u81 0.9959 0.8481 1.224 1.742 2.8115 3.2749 3.6714 3.8405 3.7159 3.561 3.7525 4.2013 4.6807 5.1294 u82 0.996 0.8473 1.2234 1.7417 2.8111 3.2735 3.6708 3.7045 3.8513 3.6126 3.77 4.2031 4.6667 5.1105 u83 0.9962 0.8471 1.2235 1.7421 2.8125 3.2739 3.6708 3.7398 3.9043 3.6307 3.759 4.2002 4.6762 5.1196 u84 0.996 0.8446 1.2206 1.7395 2.8088 3.269 3.6683 3.5864 3.7397 3.7667 3.8275 4.2295 4.6693 5.1037 u85 0.9961 0.8442 1.2213 1.7398 2.8091 3.2686 3.6676 3.565 3.7018 3.7415 3.839 4.2323 4.6591 5.0946 u86 0.9963 0.8444 1.2226 1.7409 2.8111 3.2699 3.6673 3.6717 3.609 3.6803 3.8211 4.2315 4.6737 5.1141 u87 0.9965 0.8442 1.2227 1.7411 2.8119 3.2704 3.6672 3.7095 3.6369 3.7026 3.81 4.2287 4.6835 5.1234 u88 0.9973 0.8537 1.2359 1.7568 2.8376 3.2884 3.6755 3.8446 3.7641 3.8355 3.7043 4.1008 4.5056 5.0392 u89 0.9975 0.8532 1.2366 1.7571 2.8383 3.288 3.6748 3.8013 3.7193 3.8029 3.7141 4.1051 4.4955 5.031 u90 0.9975 0.8523 1.2361 1.7567 2.8379 3.2867 3.6743 3.666 3.857 3.887 3.73 4.1029 4.4797 5.0134 u91 0.9978 0.8521 1.2361 1.7571 2.8389 3.2871 3.6743 3.7021 3.9102 3.9236 3.7203 4.0984 4.4898 5.0217 u92 0.9983 0.8541 1.2398 1.7603 2.8444 3.292 3.6759 3.9024 4.1714 3.7493 3.6567 4.0752 4.5042 5.0381 u93 0.9984 0.8536 1.2403 1.7607 2.8449 3.2916 3.6753 3.8552 4.0912 3.7198 3.6671 4.0799 4.4944 5.0301 u94 0.9986 0.854 1.2418 1.7618 2.8469 3.2929 3.6753 4.0694 3.8928 3.6527 3.6554 4.0831 4.5099 5.0476 u95 0.9988 0.8538 1.2418 1.762 2.8477 3.2933 3.6754 4.1333 3.9564 3.6776 3.6519 4.0791 4.5199 5.0558 u96 0.9968 0.937 1.5256 2.1597 2.8183 3.2753 3.6655 4.5365 4.3213 4.0144 4.3006 6.0029 6.7863 7.1885 u97 0.9966 0.9372 1.5256 2.1597 2.8189 3.2749 3.6652 4.4231 4.2037 3.9605 4.3473 5.9087 6.8606 7.1902 u98 0.9965 0.937 1.5239 2.1586 2.8184 3.2736 3.665 4.0428 4.5739 4.1035 4.4185 6.084 7.0184 7.2296 u99 0.9965 0.9377 1.5232 2.1584 2.8191 3.2739 3.6658 4.1104 4.7316 4.1698 4.365 6.2028 6.9192 7.2267 u100 0.996 0.9356 1.5181 2.1539 2.8151 3.2693 3.6634 3.8459 4.1686 4.53 4.564 6.4135 7.2596 7.4016 u101 0.9959 0.9361 1.5181 2.1539 2.8157 3.2689 3.6633 3.7996 4.0887 4.4495 4.6324 6.3018 7.3731 7.4105 u102 0.9959 0.9372 1.5193 2.1548 2.8173 3.27 3.6639 3.9715 3.8923 4.2671 4.5453 6.1274 7.1956 7.3518 u103 0.9959 0.9379 1.5186 2.1546 2.8182 3.2702 3.6647 4.0285 3.955 4.3407 4.4858 6.2267 7.0986 7.3454 u104 0.995 0.9278 1.5004 2.1329 2.796 3.2537 3.6548 3.8251 3.7601 3.9671 4.6055 5.8651 6.7617 7.4739 u105 0.9949 0.9281 1.5006 2.1329 2.7964 3.253 3.6552 3.7825 3.7159 3.9284 4.6553 5.8142 6.8076 7.4822 u106 0.9948 0.9278 1.4989 2.1319 2.7961 3.2516 3.6556 3.6586 3.8524 4.027 4.7241 5.9113 6.8926 7.5379 u107 0.9948 0.9285 1.4984 2.1318 2.7972 3.2517 3.6569 3.6938 3.9054 4.0698 4.67 5.9672 6.8407 7.5277 u108 0.9952 0.9313 1.5027 2.1359 2.8023 3.256 3.6597 3.8809 4.1603 3.8661 4.5211 5.8188 6.6438 7.3735 u109 0.9951 0.9317 1.5029 2.136 2.8026 3.2554 3.6599 3.8358 4.0813 3.8311 4.5721 5.7654 6.6862 7.3791 u110 0.9951 0.9327 1.5041 2.1369 2.8043 3.2563 3.6609 4.0319 3.8851 3.7506 4.5073 5.6716 6.6138 7.3362 u111 0.9951 0.9332 1.5034 2.1368 2.8052 3.2566 3.6618 4.0903 3.9475 3.7811 4.4615 5.7182 6.576 7.3314 u112 0.9997 0.9705 1.5989 2.2702 2.8515 3.3001 3.6717 4.5863 4.3526 4.1768 5.5558 6.0707 6.8156 8.305 u113 0.9996 0.9707 1.5987 2.2698 2.8509 3.3004 3.6703 4.4695 4.227 4.1089 5.734 5.967 6.8958 8.3953 u114 0.9995 0.9705 1.5967 2.2686 2.8496 3.2996 3.6692 4.0468 4.6126 4.2848 5.8955 6.1586 7.0601 8.6764 u115 0.9995 0.9711 1.5958 2.2682 2.8494 3.3007 3.6689 4.1028 4.7742 4.3662 5.7319 6.2881 6.9548 8.5465 u116 0.9991 0.9688 1.5906 2.2632 2.8453 3.2964 3.6657 3.8507 4.1858 4.7273 5.7188 6.4807 7.2954 8.7651 u117 0.999 0.9691 1.5905 2.2631 2.8447 3.2964 3.6645 3.8095 4.1032 4.6466 5.8238 6.3671 7.4101 8.8692 u118 0.999 0.9703 1.5913 2.2638 2.8451 3.2983 3.664 3.995 3.9005 4.4571 5.7151 6.1874 7.2309 8.6575 u119 0.999 0.9709 1.5905 2.2635 2.8449 3.2992 3.6638 4.0529 3.9647 4.5402 5.5998 6.2918 7.1312 8.5697 u120 0.9998 0.9828 1.6085 2.2865 2.863 3.3179 3.6722 4.4061 4.3635 6.2755 6.5122 7.7183 8.5647 9.5905 u121 0.9996 0.983 1.6083 2.2862 2.8621 3.3182 3.6707 4.3124 4.2323 6.3107 6.6271 7.5349 8.7598 9.9065 u122 0.9996 0.9829 1.6063 2.2848 2.8606 3.3174 3.6694 4.0197 4.622 6.1476 6.6344 7.6321 8.8941 10.0736 u123 0.9996 0.9834 1.6055 2.2845 2.86 3.3186 3.6688 4.0704 4.7846 6.1519 6.5676 7.7506 8.7552 9.8558 u124 1 0.9865 1.6099 2.2886 2.862 3.325 3.6688 4.669 6.8189 6.9881 7.7657 8.6079 10.1845 11.0225 u125 0.9999 0.9868 1.6096 2.2885 2.8611 3.3252 3.6676 4.4363 7.0127 7.248 7.4229 8.7745 9.9405 11.101 u126 0.9999 0.9879 1.6104 2.2891 2.8605 3.3277 3.6665 8.3665 8.6663 8.8291 7.9912 11.0628 10.6068 12.0247 u127 1 0.9887 1.6096 2.2886 2.8597 3.3288 3.6654 7.8601 7.9314 7.8682 9.6554 9.4334 12.514 13.9798 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 1 1 1 1 1 1 1 1.0001 1 1 1.0001 1.0002 1.0009 1.0011 u2 1.0005 1 0.9999 0.9999 1 1 1 1.0001 1 1 1.0003 1.0003 1.001 1.0016 u3 1.0006 1.0001 1 0.9999 1.0001 1 1 1.0002 0.9999 1 1.0001 1.0002 1.0002 1.0004 u4 1.0019 1.0003 0.9998 1.0003 1.0018 1.0002 1 1.0002 1.0001 1 1.0003 1.0001 1.001 1.0009 u5 1.0019 1.0003 0.9998 1.0003 1.0018 1.0002 1 1.0003 0.9999 1.0001 1.0002 1.0003 0.9999 1.0018 u6 1.0016 1.0004 1 1.0007 1.0019 1.0003 1 1.0003 0.9998 1 0.9999 1.0002 1 1.0016 u7 1.0017 1.0005 1 1.0008 1.002 1.0003 1 1.0003 0.9997 1.0002 0.9998 1.0004 1.001 1.0011 u8 1.0021 1.0028 0.9984 0.9929 0.9943 0.9993 1.0001 1.0001 0.9999 1 1.0116 1.0799 1.7515 2.723 u9 1.0021 1.0028 0.9984 0.993 0.9943 0.9994 1.0002 1.0001 0.9998 1 1.0118 1.08 1.7517 2.7234 u10 1.0025 1.0028 0.9983 0.9928 0.9943 0.9993 1.0002 1.0001 0.9998 1.0001 1.0122 1.0798 1.7514 2.7238 u11 1.0026 1.0029 0.9983 0.9929 0.9944 0.9993 1.0002 1.0002 0.9997 1.0001 1.012 1.08 1.7512 2.7237 u12 1.0014 1.0027 0.9985 0.9927 0.9928 0.9992 1.0003 1.0002 0.9996 1.0001 1.012 1.0799 1.7512 2.723 u13 1.0014 1.0027 0.9984 0.9927 0.9928 0.9992 1.0003 1.0003 0.9997 1.0002 1.012 1.0798 1.7516 2.7232 u14 1.001 1.0028 0.9984 0.9929 0.993 0.9993 1.0003 1.0003 0.9997 1.0001 1.0116 1.08 1.7515 2.7226 u15 1.001 1.0029 0.9983 0.993 0.993 0.9993 1.0003 1.0003 0.9997 1.0001 1.0118 1.0798 1.7513 2.7223 u16 0.968 0.9823 1.0031 1.0455 1.1639 1.5101 2.3862 2.821 2.9622 3.002 3.0129 3.0541 3.7157 4.7331 u17 0.968 0.9823 1.003 1.0455 1.1639 1.5101 2.3862 2.821 2.9623 3.002 3.0131 3.0549 3.7173 4.7329 u18 0.9684 0.9824 1.0029 1.0453 1.1639 1.5101 2.3862 2.8211 2.9623 3.002 3.0137 3.0547 3.7167 4.7326 u19 0.9684 0.9825 1.0028 1.0454 1.164 1.5101 2.3862 2.8211 2.9623 3.0019 3.0133 3.0548 3.716 4.7324 u20 0.9695 0.9827 1.0026 1.0457 1.1657 1.5104 2.3861 2.821 2.9623 3.002 3.0137 3.0549 3.7166 4.733 u21 0.9695 0.9827 1.0026 1.0457 1.1658 1.5104 2.3862 2.8211 2.9622 3.002 3.0136 3.0547 3.7157 4.7326 u22 0.9691 0.9828 1.0027 1.046 1.1659 1.5105 2.3862 2.8211 2.9622 3.002 3.013 3.0547 3.7165 4.7331 u23 0.9692 0.9829 1.0027 1.0461 1.166 1.5105 2.3862 2.8212 2.962 3.002 3.0129 3.0546 3.7164 4.7327 u24 0.9688 0.9809 1.0033 1.0523 1.173 1.5119 2.3862 2.8192 2.9618 3.0084 3.053 3.2258 4.6746 6.5252 u25 0.9687 0.9809 1.0034 1.0524 1.1731 1.512 2.3862 2.8192 2.9616 3.0084 3.0526 3.2258 4.6744 6.5246 u26 0.9691 0.9808 1.0033 1.0522 1.173 1.512 2.3862 2.8192 2.9617 3.0085 3.0533 3.2255 4.6745 6.525 u27 0.9691 0.9809 1.0034 1.0523 1.1731 1.512 2.3862 2.8193 2.9616 3.0085 3.0527 3.2254 4.6746 6.5254 u28 0.968 0.9807 1.0036 1.0521 1.1715 1.5118 2.3863 2.8195 2.9616 3.0086 3.0533 3.2253 4.6745 6.5264 u29 0.968 0.9807 1.0037 1.0521 1.1715 1.5118 2.3863 2.8195 2.9616 3.0086 3.0532 3.2253 4.6743 6.526 u30 0.9676 0.9807 1.0038 1.0525 1.1717 1.5119 2.3863 2.8196 2.9617 3.0086 3.0526 3.2255 4.6741 6.5256 u31 0.9676 0.9808 1.0038 1.0525 1.1718 1.5119 2.3863 2.8196 2.9616 3.0085 3.0525 3.2252 4.6741 6.5259 u32 2.7706 2.898 2.9665 3.0138 3.1134 3.4669 4.4162 4.8829 5.0326 5.0632 5.0535 5.1149 6.5671 8.569 u33 2.7702 2.8977 2.9665 3.0139 3.1135 3.4669 4.4162 4.883 5.0325 5.0632 5.0537 5.1146 6.5675 8.5693 u34 2.7711 2.8975 2.9659 3.0142 3.1139 3.467 4.4161 4.883 5.0325 5.0632 5.0541 5.1155 6.5678 8.569 u35 2.7713 2.8979 2.966 3.0143 3.1139 3.467 4.4161 4.8831 5.0325 5.0632 5.0538 5.1147 6.5667 8.5684 u36 2.7738 2.8984 2.9652 3.0111 3.1112 3.4668 4.4165 4.8831 5.0326 5.0635 5.0545 5.1147 6.567 8.5685 u37 2.7735 2.898 2.9652 3.0112 3.1113 3.4668 4.4165 4.8832 5.0326 5.0636 5.0542 5.1151 6.5675 8.5692 u38 2.7724 2.8983 2.9658 3.0111 3.1109 3.4667 4.4166 4.8832 5.0326 5.0635 5.054 5.1154 6.5674 8.5697 u39 2.7726 2.8986 2.9658 3.0111 3.1109 3.4668 4.4166 4.8832 5.0325 5.0635 5.0537 5.1145 6.5668 8.5687 u40 2.7694 2.9054 2.9863 3.0394 3.128 3.4689 4.4133 4.8794 5.0406 5.1056 5.1933 5.5323 7.8541 10.4941 u41 2.769 2.905 2.9862 3.0395 3.1281 3.4689 4.4133 4.8794 5.0405 5.1057 5.1933 5.5324 7.8541 10.4939 u42 2.77 2.9048 2.9856 3.0399 3.1285 3.4689 4.4132 4.8794 5.0406 5.1057 5.1935 5.5325 7.8538 10.4937 u43 2.7701 2.9051 2.9857 3.0399 3.1285 3.4689 4.4132 4.8794 5.0406 5.1057 5.1931 5.5324 7.8536 10.4941 u44 2.7674 2.9046 2.9864 3.0434 3.1315 3.4692 4.413 4.8794 5.0405 5.1055 5.1935 5.5323 7.8538 10.494 u45 2.7671 2.9042 2.9864 3.0435 3.1315 3.4692 4.413 4.8795 5.0405 5.1055 5.1933 5.5323 7.8541 10.4939 u46 2.766 2.9044 2.9869 3.0432 3.1312 3.4692 4.4131 4.8795 5.0406 5.1055 5.1931 5.5324 7.8542 10.4939 u47 2.7662 2.9046 2.9868 3.0432 3.1311 3.4692 4.4131 4.8795 5.0404 5.1055 5.193 5.5328 7.8543 10.4938 u48 2.8358 3.0202 3.1577 3.3064 3.615 4.4098 6.1205 6.9091 7.1543 7.1819 7.135 7.2942 9.7019 12.6145 u49 2.8354 3.0199 3.1576 3.3064 3.6151 4.4098 6.1205 6.9092 7.1543 7.1819 7.1348 7.2929 9.7021 12.614 u50 2.8363 3.0197 3.1569 3.3067 3.6159 4.4101 6.1205 6.9092 7.1543 7.182 7.1347 7.2937 9.7022 12.6142 u51 2.8365 3.02 3.1568 3.3067 3.6159 4.4103 6.1206 6.9092 7.1542 7.1819 7.1347 7.2933 9.7016 12.614 u52 2.8386 3.0206 3.156 3.3025 3.6112 4.4086 6.1204 6.9102 7.1539 7.1808 7.1345 7.2931 9.7021 12.6143 u53 2.8382 3.0204 3.156 3.3026 3.6114 4.4086 6.1203 6.9103 7.1537 7.1809 7.1345 7.2941 9.7019 12.6137 u54 2.8373 3.0206 3.1565 3.3023 3.6108 4.4084 6.1204 6.9104 7.1537 7.1808 7.1347 7.2941 9.7022 12.614 u55 2.8375 3.0209 3.1565 3.3023 3.6108 4.4086 6.1204 6.9104 7.1537 7.181 7.1347 7.2934 9.7021 12.6142 u56 2.8401 3.0149 3.1351 3.2671 3.5805 4.3956 6.1175 6.9308 7.2263 7.3626 7.5499 8.1641 11.3148 14.7279 u57 2.8397 3.0147 3.1351 3.2672 3.5806 4.3956 6.1175 6.9309 7.2262 7.3627 7.5501 8.1641 11.3145 14.7287 u58 2.8406 3.0146 3.1345 3.2675 3.5814 4.3959 6.1175 6.9309 7.2262 7.3627 7.5503 8.1644 11.3149 14.7286 u59 2.8409 3.0149 3.1345 3.2674 3.5814 4.396 6.1175 6.9309 7.2261 7.3627 7.5503 8.1643 11.3151 14.728 u60 2.8387 3.0144 3.1352 3.2716 3.5861 4.3977 6.1177 6.93 7.2265 7.364 7.5501 8.1639 11.3141 14.7282 u61 2.8384 3.0141 3.1352 3.2717 3.5863 4.3977 6.1177 6.9301 7.2266 7.3639 7.5506 8.1641 11.3144 14.7288 u62 2.8374 3.0143 3.1357 3.2714 3.5856 4.3976 6.1178 6.9302 7.2265 7.364 7.5503 8.1641 11.3137 14.7287 u63 2.8376 3.0147 3.1357 3.2713 3.5855 4.3977 6.1178 6.9303 7.2266 7.3639 7.5508 8.1637 11.3139 14.728 u64 4.9091 5.0795 5.2061 5.3107 5.5557 6.3758 8.2887 9.1665 9.4177 9.4044 9.3924 9.8362 13.2148 17.0039 u65 4.9084 5.0805 5.2066 5.3106 5.5557 6.3757 8.2885 9.1665 9.4177 9.4042 9.3926 9.8362 13.2148 17.0037 u66 4.9043 5.0813 5.2087 5.3105 5.5549 6.376 8.2899 9.1669 9.4177 9.4042 9.3918 9.8364 13.215 17.0034 u67 4.904 5.0793 5.2091 5.3108 5.555 6.3761 8.2901 9.167 9.4177 9.4041 9.392 9.836 13.2148 17.004 u68 4.8913 5.0741 5.2124 5.3207 5.5615 6.3744 8.284 9.1622 9.4196 9.4075 9.3921 9.8354 13.2144 17.0127 u69 4.8907 5.0752 5.2129 5.3207 5.5615 6.3743 8.2838 9.1622 9.4195 9.4074 9.392 9.8357 13.2149 17.0123 u70 4.8938 5.0735 5.2116 5.3212 5.5624 6.3741 8.2825 9.1618 9.4194 9.4074 9.3926 9.8356 13.2146 17.012 u71 4.8936 5.0717 5.2121 5.3216 5.5625 6.3742 8.2827 9.162 9.4194 9.4074 9.3926 9.8353 13.2155 17.0124 u72 4.8847 5.0305 5.1415 5.2473 5.5236 6.3852 8.3465 9.328 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25.7375 25.6592 25.54 27.7184 47.4854 51.2195 u50 13.2399 13.4035 13.3701 13.1998 14.6705 24.0693 25.3565 25.7358 25.6776 26.0607 29.0202 49.5433 53.4655 u51 13.2395 13.403 13.3701 13.2006 14.6701 24.0707 25.3553 25.7359 25.6743 26.0597 29.0174 49.5435 53.4582 u52 13.2404 13.4232 13.5027 13.8607 15.9969 26.129 27.545 27.9509 27.8297 27.7435 30.4166 51.6853 55.7521 u53 13.2416 13.4229 13.5031 13.861 15.9969 26.1272 27.5449 27.9527 27.8345 27.7437 30.4132 51.6875 55.7264 u54 13.2416 13.4226 13.5028 13.862 15.998 26.1264 27.5433 27.9522 27.8866 28.6142 31.7338 53.7974 58.0397 u55 13.2412 13.4229 13.5023 13.8619 15.9969 26.1297 27.5443 27.9539 27.8863 28.6058 31.7285 53.8007 58.0114 u56 15.4695 15.6354 15.5294 15.4932 17.4935 28.3018 29.7929 30.2126 30.0253 30.1633 33.1425 55.9894 60.3628 u57 15.4695 15.6359 15.5294 15.492 17.4932 28.3028 29.7933 30.2117 30.0251 30.1586 33.1369 55.99 60.3492 u58 15.4698 15.6351 15.5295 15.4926 17.4933 28.3013 29.7925 30.2145 30.1545 31.2927 34.5363 58.1615 62.684 u59 15.47 15.6345 15.5299 15.4944 17.4936 28.302 29.7914 30.2159 30.1555 31.2986 34.5258 58.1607 62.6805 u60 15.4822 15.7086 15.8746 16.5486 18.9258 30.4642 32.081 32.5124 32.2268 32.7848 35.9852 60.3904 65.0661 u61 15.4818 15.7082 15.8741 16.5476 18.9261 30.465 32.08 32.5102 32.2223 32.7812 35.9871 60.3926 65.0532 u62 15.4822 15.7077 15.8736 16.5474 18.927 30.4705 32.0774 32.524 32.5194 34.0615 37.3989 62.6197 67.4533 u63 15.4821 15.7077 15.8741 16.5498 18.9263 30.4707 32.0782 32.5252 32.525 34.0601 37.4058 62.6194 67.45 u64 17.8039 17.9235 17.7749 18.0908 20.4681 32.7308 34.4285 34.8508 34.4638 35.5387 38.8801 64.9059 69.8435 u65 17.8033 17.9229 17.775 18.0916 20.4684 32.7342 34.4286 34.8517 34.4716 35.5407 38.8762 64.9012 69.8618 u66 17.8036 17.9233 17.7746 18.0899 20.4691 32.7353 34.4319 34.8946 35.0611 36.9021 40.3523 67.197 72.2732 u67 17.8046 17.9235 17.7746 18.09 20.4684 32.7374 34.4325 34.8942 35.0559 36.8974 40.3446 67.1931 72.2674 u68 17.8596 18.1519 18.5207 19.4231 22.0024 35.0307 36.8304 37.2229 36.8551 38.383 41.8603 69.536 74.7596 u69 17.8589 18.1531 18.5216 19.4233 22.0024 35.0258 36.832 37.2222 36.8551 38.3841 41.8594 69.5345 74.7295 u70 17.8584 18.1533 18.5209 19.4215 22.0014 35.0353 36.8376 37.3434 37.8414 39.8194 43.3968 71.8934 77.2584 u71 17.8591 18.1523 18.5212 19.4214 22.0026 35.0373 36.8413 37.3441 37.8414 39.818 43.4039 71.8922 77.2299 u72 20.2138 20.2778 20.2921 20.9646 23.6204 37.4258 39.2979 39.6172 39.5116 41.3494 44.9547 74.3042 79.794 u73 20.2143 20.2777 20.2924 20.9666 23.6212 37.4258 39.2979 39.6173 39.509 41.3364 44.9503 74.3063 79.7739 u74 20.2146 20.2783 20.2923 20.9653 23.6208 37.4354 39.3284 39.9222 40.8043 42.8419 46.5098 76.7413 82.3524 u75 20.2144 20.2769 20.292 20.9651 23.6208 37.432 39.3274 39.9226 40.8082 42.8464 46.486 76.7436 82.3657 u76 20.42 20.8736 21.5286 22.4713 25.2716 39.8894 41.819 42.0625 42.4198 44.4117 48.1059 79.225 84.9825 u77 20.4194 20.8739 21.5305 22.4715 25.2701 39.8807 41.8165 42.0611 42.4209 44.4134 48.0959 79.2238 84.9999 u78 20.4194 20.8736 21.5298 22.4719 25.2715 39.8945 41.9135 42.7227 43.8895 45.9884 49.697 81.7531 87.6215 u79 20.4195 20.8732 21.5288 22.472 25.2723 39.9024 41.9126 42.7223 43.8897 45.9742 49.7094 81.7468 87.6724 u80 22.7233 22.8704 23.2313 24.0926 26.9965 42.4275 44.3814 44.7027 45.527 47.6023 51.3549 84.3422 90.3187 u81 22.7236 22.8711 23.2304 24.0923 27.0001 42.4321 44.3853 44.7029 45.5275 47.601 51.3717 84.3288 90.4311 u82 22.7246 22.8715 23.2302 24.0924 27.0041 42.4692 44.6426 45.8431 47.1136 49.2392 53.0585 86.9802 93.0428 u83 22.7242 22.8705 23.2313 24.0935 27.0015 42.461 44.6417 45.8431 47.103 49.2363 53.0737 86.9711 93.2898 u84 23.3138 24.0541 24.8112 25.751 28.7832 45.0533 47.0001 47.6949 48.7801 50.9199 54.7968 89.6586 95.801 u85 23.3127 24.0543 24.8118 25.751 28.7794 45.045 46.9988 47.696 48.7776 50.9245 54.807 89.6655 96.2763 u86 23.3144 24.0547 24.8116 25.7552 28.8014 45.1577 47.6181 49.2057 50.4537 52.6302 56.5811 92.3763 98.6388 u87 23.313 24.0544 24.8109 25.7544 28.8046 45.1638 47.6189 49.2068 50.4564 52.643 56.5866 92.4194 99.5106 u88 25.5044 25.9653 26.5789 27.5038 30.6332 47.7278 49.8108 51.0227 52.2038 54.4034 58.3896 95.1312 101.6507 u89 25.5051 25.9648 26.5791 27.5029 30.6352 47.725 49.8118 51.0229 52.1989 54.4037 58.3844 95.2633 103.0069 u90 25.5053 25.964 26.5809 27.52 30.7141 48.0599 50.9801 52.7432 53.9696 56.2267 60.2319 97.9117 105.0269 u91 25.5049 25.9644 26.5807 27.521 30.7134 48.0654 50.9816 52.7453 53.9632 56.2216 60.2299 98.2343 106.631 u92 26.7816 27.6749 28.3939 29.3219 32.5364 50.5027 53.035 54.6113 55.8117 58.0789 62.0692 100.7297 108.6317 u93 26.7831 27.6761 28.3935 29.3221 32.5365 50.51 53.0336 54.6119 55.8027 58.0845 62.1495 101.4149 110.3993 u94 26.7809 27.6769 28.4103 29.3929 32.7789 51.2992 54.6924 56.4831 57.7006 59.9745 63.9313 103.7252 112.3836 u95 26.7811 27.6774 28.4104 29.3936 32.7792 51.2959 54.694 56.4803 57.7011 60.0062 64.1876 104.9305 114.3191 u96 28.9133 29.6554 30.3268 31.2106 34.5196 53.5865 56.7122 58.4546 59.6618 61.925 65.8707 107.0741 116.3731 u97 28.9131 29.655 30.3276 31.2106 34.5185 53.5784 56.7123 58.4533 59.6589 61.9994 66.3884 108.7177 118.3829 u98 28.9139 29.6732 30.4037 31.4462 35.1081 55.0276 58.6598 60.4712 61.6726 63.8904 67.956 110.7913 120.5016 u99 28.9145 29.6736 30.403 31.4444 35.1106 55.0302 58.6585 60.4736 61.6878 64.0956 68.8364 112.6798 122.6396 u100 30.8635 31.7009 32.3378 33.1867 36.7457 57.2064 60.7699 62.5823 63.7283 65.9028 70.2821 114.777 124.8491 u101 30.8637 31.7021 32.3379 33.1877 36.746 57.2057 60.7722 62.5903 63.8097 66.3942 71.4289 116.8115 127.09 u102 30.8923 31.7987 32.602 33.7894 37.832 59.1583 62.9276 64.7595 65.8345 68.061 72.8718 118.9684 129.3915 u103 30.8921 31.7987 32.602 33.7912 37.8322 59.1589 62.9305 64.7912 66.0432 68.9522 74.1587 121.1169 131.7078 u104 33.1103 33.8833 34.4773 35.4425 39.4064 61.3827 65.2053 67.011 67.9846 70.5191 75.6001 123.3634 134.0697 u105 33.1098 33.8828 34.4762 35.442 39.4075 61.3888 65.2239 67.1249 68.4883 71.7518 77.0182 125.6343 136.4748 u106 33.2559 34.2269 35.172 36.5807 40.8735 63.6481 67.5701 69.3232 70.2982 73.2724 78.5537 127.9882 138.9739 u107 33.2568 34.2274 35.1737 36.5807 40.8734 63.659 67.6342 69.6384 71.2727 74.709 80.0777 130.3969 141.5291 u108 35.4684 36.2481 36.9718 38.1902 42.5213 66.0718 70.0278 71.7242 72.9705 76.2561 81.6684 132.8873 144.1989 u109 35.4689 36.2489 36.9721 38.1901 42.5275 66.119 70.2374 72.4646 74.349 77.8245 83.2755 135.4437 146.9255 u110 35.9949 37.1526 38.3017 39.7394 44.2273 68.5974 72.5659 74.4167 76.0146 79.477 84.9523 138.085 149.7421 u111 35.9934 37.1496 38.3007 39.7481 44.2665 68.7677 73.131 75.7125 77.646 81.161 86.7073 140.8074 152.6113 u112 38.1816 39.1352 40.0935 41.4613 46.0376 71.2182 75.3271 77.574 79.3964 82.93 88.4865 143.626 155.5662 u113 38.1774 39.1335 40.1039 41.516 46.1905 71.7293 76.5081 79.2732 81.1921 84.7563 90.3453 146.5311 158.5759 u114 39.4601 40.7841 41.8845 43.2609 47.9278 74.0577 78.5907 81.1887 83.092 86.6595 92.2971 149.5326 161.6944 u115 39.4654 40.8108 41.9638 43.4675 48.3853 75.2231 80.3611 83.1387 85.0706 88.6446 94.3202 152.6251 164.8804 u116 41.6592 42.8235 43.8418 45.1833 50.0471 77.4591 82.4633 85.2176 87.1495 90.7162 96.3936 155.829 168.1631 u117 41.7049 42.9554 44.136 45.7703 51.0365 79.3386 84.5973 87.3964 89.3121 92.8734 98.5482 159.1453 171.495 u118 43.7517 44.9531 45.9711 47.4293 52.6487 81.6178 86.9047 89.7118 91.5981 95.1252 100.7916 162.5723 174.9686 u119 44.0261 45.4435 46.7742 48.6159 54.1387 83.9545 89.3582 92.1643 93.9938 97.4803 103.1416 166.1155 178.531 u120 46.1915 47.437 48.591 50.2795 55.8617 86.5324 91.9868 94.7707 96.529 99.9355 105.5792 169.8029 182.2238 u121 47.0297 48.6433 50.122 51.9653 57.7109 89.2947 94.8013 97.5359 99.1736 102.4958 108.1276 173.63 186.0831 u122 49.2467 50.6869 52.0513 53.8713 59.739 92.3002 97.8188 100.4667 101.982 105.1988 110.8224 177.6145 190.0792 u123 51.1141 52.7512 54.165 55.9764 61.9603 95.5521 101.0594 103.5869 104.9459 108.0373 113.5985 181.7798 194.231 u124 53.5989 55.1926 56.557 58.314 64.3981 99.1007 104.5481 106.9211 108.0924 111.0473 116.55 186.1633 198.5898 u125 56.464 57.9913 59.2563 60.9174 67.0836 102.97 108.3322 110.5136 111.4395 114.2481 119.6945 190.8022 203.2222 u126 59.8456 61.2264 62.3312 63.8479 70.0819 107.2526 112.4929 114.4357 115.113 117.7127 123.0838 195.7743 208.1804 u127 63.9379 65.0834 65.9472 67.2579 73.5415 112.162 117.228 118.8617 119.2181 121.5705 127.0239 201.2647 213.6522

h) 262144-QAM/512-PAM for a Non-Fading Channel

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9998 1.0001 0.9999 1 1.0006 0.9995 0.9998 0.9962 1.0007 0.9963 1.0006 1.0006 1.0001 1.0001 u2 0.9991 0.9999 0.9995 0.9997 1.001 0.9988 0.9997 0.9948 0.9893 0.9887 0.996 0.9998 1.0003 1.0007 u3 0.9986 1 0.9994 0.9995 1.0016 0.9985 0.9996 0.9944 0.9902 0.9926 0.9952 0.9985 1 1.0007 u4 0.9978 0.9994 0.9986 0.999 1.0019 0.9979 0.9995 0.9893 0.9616 0.9733 0.9889 0.9943 1.0001 1.0018 u5 0.9973 0.9995 0.9985 0.9989 1.0022 0.9973 0.9994 0.9847 0.9623 0.9695 0.9896 0.9947 1.0003 1.0019 u6 0.9968 0.9998 0.9986 0.9989 1.0027 0.9969 0.9993 0.9818 0.9746 0.9772 0.9941 0.9946 1 1.0014 u7 0.9963 0.9998 0.9985 0.9987 1.0031 0.9963 0.9993 0.9813 0.9759 0.9811 0.9934 0.9934 0.9997 1.0015 u8 0.9946 0.9971 0.9963 0.9971 1.0033 0.9958 0.9994 1.0291 1.0236 0.951 0.976 0.986 0.9983 1.0018 u9 0.9943 0.9972 0.9962 0.9971 1.0037 0.9954 0.9993 1.0269 1.0243 0.9469 0.9767 0.9864 0.9985 1.0019 u10 0.9937 0.997 0.9958 0.9968 1.0042 0.995 0.9994 1.027 1.0124 0.9389 0.9724 0.9855 0.9987 1.0024 u11 0.9932 0.9971 0.9957 0.9967 1.0046 0.9945 0.9993 1.0276 1.0134 0.9423 0.9718 0.9844 0.9984 1.0025 u12 0.993 0.9978 0.9961 0.9969 1.0052 0.994 0.9993 1.0254 1.0456 0.9621 0.9779 0.9877 0.9981 1.0015 u13 0.9926 0.9978 0.996 0.9968 1.0055 0.9937 0.9993 1.0234 1.0463 0.958 0.9786 0.9884 0.9983 1.0015 u14 0.992 0.9981 0.9961 0.9969 1.006 0.9931 0.9992 1.0218 1.0597 0.9656 0.983 0.9884 0.9981 1.0011 u15 0.9917 0.9982 0.996 0.9966 1.0064 0.9929 0.9993 1.0217 1.0609 0.9694 0.9825 0.987 0.9978 1.0011 u16 0.9854 0.9856 0.986 0.9894 1.0047 0.9922 1.0001 1.0799 1.1302 1.0696 0.9687 0.9919 0.9883 0.9939 u17 0.9851 0.9857 0.9859 0.9893 1.0052 0.992 1.0001 1.0788 1.13 1.0655 0.9694 0.9924 0.9887 0.9939 u18 0.9844 0.9855 0.9855 0.9891 1.0055 0.9915 1.0002 1.0801 1.1161 1.0572 0.9648 0.9918 0.989 0.9944 u19 0.9841 0.9856 0.9854 0.989 1.006 0.9911 1.0002 1.0822 1.1164 1.0616 0.9642 0.9906 0.9889 0.9944 u20 0.9832 0.985 0.9847 0.9885 1.0064 0.9907 1.0003 1.0831 1.082 1.0407 0.9578 0.9869 0.9893 0.9955 u21 0.9826 0.9851 0.9846 0.9884 1.0066 0.9903 1.0003 1.0824 1.0818 1.0367 0.9585 0.9873 0.9896 0.9955 u22 0.9823 0.9854 0.9847 0.9884 1.0071 0.9899 1.0003 1.082 1.0954 1.0455 0.963 0.9873 0.9895 0.995 u23 0.9819 0.9854 0.9845 0.9883 1.0076 0.9897 1.0004 1.084 1.0957 1.0499 0.9624 0.9862 0.9894 0.995 u24 0.9826 0.9883 0.9865 0.9895 1.0085 0.9893 1.0002 1.0321 1.043 1.0838 0.9801 0.9923 0.9908 0.9947 u25 0.9822 0.9884 0.9863 0.9895 1.009 0.9889 1.0003 1.0311 1.0428 1.0797 0.9807 0.993 0.991 0.9947 u26 0.9818 0.9882 0.9859 0.9892 1.0093 0.9886 1.0004 1.0323 1.0299 1.0712 0.9762 0.9924 0.9913 0.9952 u27 0.9811 0.9882 0.9858 0.989 1.0097 0.9884 1.0004 1.0341 1.0301 1.0757 0.9755 0.9914 0.9911 0.9952 u28 0.9809 0.9889 0.9863 0.9894 1.0102 0.9879 1.0004 1.033 1.0628 1.0979 0.9817 0.9953 0.9908 0.9942 u29 0.9804 0.989 0.9861 0.9893 1.0105 0.9876 1.0004 1.0322 1.0626 1.0938 0.9824 0.9961 0.991 0.9942 u30 0.9801 0.9893 0.9862 0.9892 1.0109 0.9873 1.0005 1.0313 1.0758 1.1029 0.9868 0.9964 0.9909 0.9937 u31 0.9797 0.9894 0.9862 0.9891 1.0113 0.987 1.0006 1.0331 1.076 1.1074 0.9861 0.9954 0.9906 0.9937 u32 0.9865 0.9479 0.9445 0.9566 0.9978 0.9938 1.0006 1.0721 1.1533 1.2466 1.1002 1.0032 0.978 0.9669 u33 0.9859 0.948 0.9444 0.9565 0.998 0.9937 1.0007 1.0709 1.1531 1.2416 1.1011 1.0042 0.9782 0.9671 u34 0.9856 0.9479 0.9441 0.9564 0.9983 0.9936 1.0008 1.0722 1.1392 1.2318 1.0958 1.0037 0.9783 0.9678 u35 0.985 0.9479 0.944 0.9563 0.9985 0.9935 1.0009 1.0743 1.1395 1.2365 1.0951 1.0028 0.9781 0.9678 u36 0.9844 0.9474 0.9434 0.9559 0.9987 0.9933 1.001 1.0749 1.1049 1.2124 1.0878 0.9984 0.9781 0.969 u37 0.9841 0.9475 0.9433 0.9558 0.9988 0.9931 1.0011 1.0737 1.1047 1.2076 1.0887 0.9994 0.9783 0.9691 u38 0.9837 0.9477 0.9434 0.9559 0.9991 0.9931 1.0011 1.073 1.1186 1.2173 1.0941 0.9998 0.9782 0.9686 u39 0.9833 0.9478 0.9434 0.9559 0.9993 0.993 1.0012 1.0751 1.1188 1.222 1.0933 0.9989 0.9781 0.9686 u40 0.9818 0.9453 0.9415 0.9545 0.9991 0.9927 1.0014 1.125 1.1761 1.186 1.0734 0.9913 0.9756 0.9692 u41 0.9813 0.9454 0.9413 0.9545 0.9993 0.9926 1.0014 1.1235 1.1759 1.1814 1.0742 0.9922 0.9758 0.9693 u42 0.981 0.9452 0.9411 0.9543 0.9994 0.9925 1.0015 1.1245 1.1615 1.1717 1.069 0.9919 0.976 0.9698 u43 0.9806 0.9453 0.941 0.9542 0.9996 0.9924 1.0015 1.1264 1.1617 1.1764 1.0682 0.991 0.9758 0.9697 u44 0.9805 0.9459 0.9414 0.9545 1 0.9922 1.0014 1.126 1.1979 1.2004 1.0754 0.9952 0.9759 0.9685 u45 0.9801 0.946 0.9413 0.9545 1.0002 0.9921 1.0014 1.1245 1.1977 1.1957 1.0762 0.9961 0.9761 0.9686 u46 0.9797 0.9462 0.9414 0.9546 1.0004 0.992 1.0014 1.1237 1.2122 1.2055 1.0814 0.9965 0.9761 0.968 u47 0.9793 0.9463 0.9413 0.9545 1.0006 0.9918 1.0014 1.1254 1.2124 1.2103 1.0806 0.9956 0.9759 0.9678 u48 0.9841 0.9581 0.9503 0.9609 1.0031 0.9919 1.0012 1.0813 1.1302 1.0859 1.0919 0.9951 0.987 0.9726 u49 0.9836 0.9581 0.9502 0.9609 1.0034 0.9917 1.0012 1.0799 1.1299 1.0817 1.0927 0.996 0.9872 0.9725 u50 0.9832 0.958 0.9498 0.9607 1.0035 0.9916 1.0011 1.0808 1.1161 1.0733 1.0873 0.9956 0.9873 0.973 u51 0.9829 0.958 0.9498 0.9606 1.0038 0.9914 1.0011 1.0823 1.1162 1.0778 1.0864 0.9947 0.9871 0.9729 u52 0.982 0.9575 0.9492 0.9602 1.0039 0.9911 1.001 1.0826 1.082 1.0566 1.0791 0.9905 0.9873 0.9739 u53 0.9816 0.9576 0.9491 0.9602 1.0041 0.991 1.001 1.0808 1.0818 1.0526 1.0798 0.9915 0.9874 0.9738 u54 0.9814 0.9578 0.9492 0.9602 1.0043 0.9908 1.0009 1.0799 1.0953 1.0616 1.085 0.992 0.9872 0.9732 u55 0.981 0.9578 0.9492 0.9601 1.0045 0.9906 1.0008 1.0814 1.0955 1.0662 1.0841 0.9911 0.987 0.9731 u56 0.9816 0.9605 0.9509 0.9613 1.0053 0.9904 1.0005 1.0319 1.043 1.0994 1.1042 0.9995 0.9881 0.9724 u57 0.9811 0.9606 0.9508 0.9613 1.0055 0.9902 1.0004 1.03 1.0429 1.0955 1.105 1.0005 0.9882 0.9723 u58 0.9806 0.9604 0.9505 0.9612 1.0056 0.99 1.0003 1.0307 1.0301 1.0873 1.0994 1.0001 0.9884 0.9728 u59 0.9803 0.9604 0.9505 0.961 1.0059 0.9897 1.0002 1.0317 1.0304 1.092 1.0984 0.9992 0.9881 0.9726 u60 0.9801 0.9611 0.9509 0.9614 1.0062 0.9895 0.9999 1.0314 1.0628 1.1143 1.1056 1.0034 0.9878 0.9714 u61 0.9799 0.9612 0.9508 0.9614 1.0065 0.9893 0.9998 1.0293 1.0627 1.1105 1.1063 1.0044 0.9879 0.9714 u62 0.9794 0.9614 0.9509 0.9614 1.0068 0.989 0.9996 1.0283 1.0759 1.12 1.1115 1.0048 0.9876 0.9709 u63 0.979 0.9615 0.9509 0.9613 1.007 0.9888 0.9994 1.029 1.0761 1.1252 1.1105 1.0039 0.9873 0.9708 u64 0.9546 0.8578 0.8134 0.8471 1.0124 0.9912 1.0025 1.0806 1.161 1.2656 1.5203 1.8256 2.2149 2.5504 u65 0.9563 0.8584 0.8137 0.8475 1.0117 0.9912 1.0023 1.0785 1.1604 1.2606 1.5216 1.8285 2.215 2.5507 u66 0.9572 0.8587 0.8139 0.8478 1.0113 0.9913 1.002 1.0786 1.146 1.2502 1.5147 1.827 2.2141 2.5515 u67 0.9585 0.859 0.814 0.8481 1.0109 0.9915 1.0018 1.0792 1.146 1.2546 1.5134 1.8241 2.2139 2.5512 u68 0.9591 0.8589 0.8139 0.848 1.0104 0.9915 1.0016 1.0787 1.1109 1.2303 1.5041 1.8141 2.2107 2.5522 u69 0.9603 0.8595 0.8142 0.8484 1.01 0.9916 1.0013 1.0764 1.1103 1.2251 1.5054 1.8169 2.2108 2.5525 u70 0.9615 0.86 0.8148 0.8489 1.0095 0.9917 1.0011 1.0748 1.1239 1.2344 1.5123 1.8183 2.2117 2.5516 u71 0.9624 0.8606 0.8152 0.8491 1.009 0.9919 1.0009 1.0756 1.1238 1.239 1.511 1.8155 2.2115 2.5513 u72 0.9628 0.8587 0.8138 0.8485 1.0085 0.9915 1.0006 1.1257 1.1816 1.2024 1.4871 1.8008 2.2027 2.5496 u73 0.9637 0.8591 0.8141 0.8487 1.0081 0.9916 1.0004 1.1238 1.181 1.1973 1.4884 1.8036 2.2029 2.5498 u74 0.9647 0.8594 0.8143 0.8489 1.0075 0.9918 1.0002 1.1242 1.1663 1.1874 1.4814 1.8021 2.2019 2.5506 u75 0.9661 0.86 0.8146 0.8493 1.0072 0.9919 1.0001 1.1254 1.1663 1.1917 1.4802 1.7993 2.2017 2.5503 u76 0.9672 0.8608 0.8154 0.85 1.0067 0.9922 0.9999 1.1242 1.2023 1.2154 1.4896 1.8092 2.2048 2.5492 u77 0.9684 0.8613 0.8157 0.8503 1.0061 0.9923 0.9997 1.1223 1.2018 1.2103 1.4908 1.812 2.205 2.5494 u78 0.97 0.8619 0.8162 0.8506 1.0058 0.9925 0.9995 1.121 1.2161 1.2199 1.4978 1.8135 2.2058 2.5485 u79 0.9709 0.8626 0.8165 0.851 1.0052 0.9927 0.9994 1.1222 1.2161 1.2243 1.4965 1.8106 2.2056 2.5482 u80 0.967 0.853 0.8095 0.8458 1.004 0.9908 0.9993 1.1692 1.302 1.3625 1.4833 1.8295 2.2012 2.5365 u81 0.9684 0.8535 0.8097 0.8461 1.0037 0.991 0.9992 1.1674 1.3015 1.3569 1.4847 1.8325 2.2014 2.5367 u82 0.9693 0.8539 0.8099 0.8463 1.0031 0.9912 0.9991 1.1681 1.2864 1.3461 1.4776 1.831 2.2005 2.5375 u83 0.9707 0.8543 0.8104 0.8467 1.0024 0.9914 0.999 1.1695 1.2865 1.3506 1.4764 1.828 2.2002 2.5372 u84 0.9721 0.8543 0.8102 0.8467 1.002 0.9915 0.9988 1.1704 1.249 1.3252 1.4668 1.8176 2.1969 2.5383 u85 0.9728 0.8548 0.8106 0.8471 1.0015 0.9917 0.9987 1.1685 1.2486 1.3196 1.4681 1.8205 2.1971 2.5385 u86 0.9741 0.8555 0.8112 0.8476 1.0011 0.9919 0.9986 1.1676 1.2633 1.3294 1.4752 1.822 2.198 2.5376 u87 0.9753 0.856 0.8114 0.8479 1.0005 0.9922 0.9985 1.1689 1.2634 1.3341 1.474 1.819 2.1978 2.5373 u88 0.9772 0.8586 0.8133 0.8492 1.0002 0.9929 0.9984 1.1157 1.2016 1.3715 1.4985 1.8345 2.2069 2.5389 u89 0.9786 0.859 0.8135 0.8496 0.9996 0.9931 0.9984 1.1139 1.2012 1.3662 1.4998 1.8375 2.2071 2.5391 u90 0.9799 0.8594 0.8138 0.8499 0.9991 0.9933 0.9983 1.1146 1.1864 1.3558 1.4927 1.8359 2.2061 2.5399 u91 0.9808 0.86 0.8141 0.8501 0.9987 0.9935 0.9982 1.1159 1.1864 1.3605 1.4914 1.8329 2.2059 2.5396 u92 0.9819 0.8608 0.8147 0.8507 0.9984 0.9939 0.9982 1.1145 1.2226 1.3855 1.5009 1.8433 2.2092 2.5384 u93 0.9829 0.8615 0.8151 0.851 0.998 0.9942 0.9981 1.1126 1.2223 1.3803 1.5021 1.8463 2.2095 2.5386 u94 0.9844 0.8619 0.8155 0.8514 0.9973 0.9944 0.9981 1.1116 1.2367 1.3903 1.5092 1.8478 2.2104 2.5377 u95 0.9854 0.8625 0.8159 0.8518 0.9969 0.9946 0.998 1.1129 1.2367 1.3952 1.5079 1.8448 2.2102 2.5374 u96 0.9694 0.8911 0.8434 0.8758 1.0064 0.9966 1.0017 1.0786 1.1574 1.2454 1.3448 1.8091 2.2111 2.5636 u97 0.9696 0.8915 0.8435 0.8759 1.0063 0.9967 1.0016 1.0766 1.1571 1.2407 1.3458 1.812 2.2112 2.5638 u98 0.9701 0.8914 0.8434 0.876 1.0062 0.9967 1.0015 1.077 1.1429 1.231 1.3391 1.8106 2.2102 2.5645 u99 0.9707 0.8917 0.8435 0.8761 1.006 0.9967 1.0014 1.0784 1.1431 1.2358 1.3379 1.8078 2.21 2.5642 u100 0.9709 0.8915 0.8432 0.8759 1.0058 0.9967 1.0013 1.0781 1.1081 1.2119 1.3289 1.7981 2.2065 2.5652 u101 0.9714 0.8917 0.8433 0.8761 1.0056 0.9968 1.0012 1.0763 1.1078 1.2073 1.3299 1.8009 2.2067 2.5654 u102 0.9718 0.8921 0.8435 0.8763 1.0055 0.9968 1.0012 1.0751 1.1215 1.217 1.3363 1.8023 2.2075 2.5645 u103 0.9724 0.8923 0.8437 0.8764 1.0054 0.9969 1.0011 1.0766 1.1216 1.2219 1.3351 1.7995 2.2072 2.5642 u104 0.9721 0.8904 0.8423 0.8755 1.0047 0.9968 1.0011 1.126 1.1789 1.1859 1.311 1.7851 2.1982 2.5625 u105 0.9726 0.8906 0.8424 0.8757 1.0047 0.9968 1.0011 1.1242 1.1786 1.1812 1.3119 1.7878 2.1983 2.5627 u106 0.9729 0.8907 0.8423 0.8757 1.0045 0.9969 1.0011 1.1248 1.1641 1.1717 1.3054 1.7865 2.1973 2.5634 u107 0.9735 0.8909 0.8424 0.8758 1.0043 0.9969 1.001 1.1264 1.1642 1.1765 1.3041 1.7838 2.197 2.5631 u108 0.9739 0.8917 0.8429 0.8762 1.0044 0.997 1.0008 1.1258 1.2003 1.2005 1.313 1.7935 2.2002 2.5621 u109 0.9743 0.8919 0.843 0.8763 1.0043 0.9971 1.0008 1.124 1.2 1.1958 1.314 1.7963 2.2003 2.5623 u110 0.9748 0.8923 0.8432 0.8764 1.0042 0.9971 1.0007 1.123 1.2145 1.2057 1.3204 1.7977 2.2011 2.5615 u111 0.9753 0.8924 0.8433 0.8766 1.0041 0.9972 1.0007 1.1244 1.2146 1.2105 1.3192 1.795 2.2007 2.5612 u112 0.9785 0.9026 0.8506 0.8818 1.0069 0.9975 1 1.0788 1.1336 1.0874 1.3348 1.7774 2.2054 2.5719 u113 0.979 0.9028 0.8506 0.8819 1.0069 0.9975 1 1.0771 1.1333 1.083 1.3358 1.7802 2.2054 2.5721 u114 0.9791 0.9028 0.8505 0.8819 1.0069 0.9975 0.9999 1.0777 1.1194 1.0743 1.3292 1.7789 2.2043 2.5728 u115 0.9794 0.903 0.8506 0.882 1.0068 0.9975 0.9998 1.0792 1.1196 1.0785 1.3281 1.7764 2.2039 2.5725 u116 0.9797 0.9026 0.8502 0.8817 1.0067 0.9975 0.9998 1.0794 1.0852 1.057 1.3192 1.7672 2.2006 2.5733 u117 0.98 0.9029 0.8502 0.8819 1.0066 0.9975 0.9998 1.0776 1.085 1.0527 1.3202 1.77 2.2007 2.5735 u118 0.9802 0.9032 0.8504 0.882 1.0067 0.9975 0.9998 1.0766 1.0985 1.0613 1.3266 1.7714 2.2014 2.5727 u119 0.9805 0.9034 0.8505 0.882 1.0066 0.9975 0.9997 1.0782 1.0987 1.0653 1.3255 1.7689 2.201 2.5724 u120 0.9812 0.9057 0.8519 0.883 1.0073 0.9974 0.9995 1.0278 1.0461 1.0986 1.3492 1.7829 2.2093 2.574 u121 0.9817 0.9059 0.852 0.8831 1.0074 0.9974 0.9994 1.0262 1.0459 1.0943 1.3502 1.7857 2.2093 2.5742 u122 0.9818 0.9058 0.8518 0.883 1.0074 0.9974 0.9993 1.0267 1.0331 1.0854 1.3437 1.7844 2.2082 2.5749 u123 0.982 0.906 0.8519 0.883 1.0073 0.9973 0.9993 1.0282 1.0332 1.0896 1.3425 1.7819 2.2079 2.5746 u124 0.9823 0.9067 0.8523 0.8833 1.0075 0.9973 0.9991 1.0282 1.0658 1.1117 1.3513 1.7914 2.2109 2.5736 u125 0.9826 0.9068 0.8523 0.8834 1.0076 0.9972 0.9991 1.0265 1.0656 1.1073 1.3524 1.7942 2.211 2.5738 u126 0.9828 0.9071 0.8524 0.8834 1.0077 0.9972 0.999 1.0255 1.0788 1.1162 1.3588 1.7956 2.2116 2.573 u127 0.9831 0.9073 0.8525 0.8834 1.0077 0.9971 0.9989 1.0271 1.079 1.1206 1.3577 1.7931 2.2112 2.5727 u128 0.9756 0.8808 1.3017 1.8444 2.8725 3.3532 3.6746 4.2319 4.1112 3.9432 3.6724 3.9399 4.3558 4.686 u129 0.9757 0.8809 1.3017 1.8447 2.8733 3.3528 3.6745 4.2775 4.1131 3.9693 3.6742 3.9449 4.3544 4.6854 u130 0.9758 0.8809 1.3015 1.8444 2.874 3.3524 3.6745 4.2579 4.2341 4.026 3.684 3.9415 4.3493 4.6802 u131 0.9758 0.8809 1.3016 1.8445 2.8748 3.3523 3.6745 4.22 4.232 3.9977 3.6824 3.937 4.3523 4.6794 u132 0.9757 0.8806 1.3008 1.8436 2.8746 3.3508 3.6742 4.3134 4.6448 4.1662 3.7017 3.9349 4.3357 4.6658 u133 0.9757 0.8807 1.3009 1.8439 2.8754 3.3506 3.6742 4.3572 4.6481 4.2022 3.7035 3.94 4.3343 4.6649 u134 0.9757 0.8809 1.3015 1.8444 2.8767 3.3506 3.6743 4.3836 4.4679 4.1318 3.6933 3.944 4.3414 4.6687 u135 0.9758 0.881 1.3016 1.8444 2.8776 3.3506 3.6743 4.3461 4.4653 4.0993 3.6917 3.9392 4.3442 4.6675 u136 0.9752 0.879 1.2986 1.841 2.8735 3.3447 3.6734 3.854 4.1292 4.4207 3.7812 3.9556 4.3214 4.6541 u137 0.9752 0.8791 1.2987 1.8412 2.8745 3.3444 3.6734 3.876 4.1308 4.462 3.7826 3.9608 4.3194 4.6534 u138 0.975 0.879 1.2985 1.841 2.8752 3.344 3.6733 3.8631 4.2298 4.5456 3.7964 3.9569 4.3128 4.6483 u139 0.975 0.8791 1.2987 1.8411 2.8761 3.344 3.6733 3.8404 4.228 4.5024 3.795 3.9516 4.3149 4.6474 u140 0.9751 0.8796 1.2996 1.8422 2.8781 3.345 3.6736 3.7681 3.9867 4.3011 3.7699 3.9548 4.3325 4.6596 u141 0.9751 0.8798 1.2998 1.8425 2.8791 3.3448 3.6736 3.7892 3.988 4.3395 3.7713 3.96 4.3305 4.6591 u142 0.975 0.88 1.3003 1.8429 2.88 3.3449 3.6736 3.8007 3.9117 4.2646 3.7585 3.9641 4.3372 4.663 u143 0.9749 0.8801 1.3004 1.843 2.8812 3.3448 3.6737 3.7784 3.9105 4.2291 3.757 3.9589 4.3394 4.6621 u144 0.9705 0.8702 1.2859 1.8261 2.8536 3.3242 3.6705 3.5727 3.7017 3.8676 3.9123 4.0804 4.4853 4.7149 u145 0.9703 0.8703 1.2861 1.8264 2.8544 3.3239 3.6704 3.5878 3.7023 3.8844 3.913 4.0851 4.483 4.715 u146 0.9699 0.8702 1.2859 1.8262 2.8548 3.3235 3.6703 3.5797 3.7505 3.9198 3.93 4.0812 4.4762 4.7102 u147 0.9697 0.8702 1.286 1.8263 2.8558 3.3234 3.6704 3.5648 3.7496 3.9015 3.9293 4.0764 4.4788 4.7102 u148 0.9692 0.8698 1.2853 1.8254 2.8554 3.322 3.67 3.6212 3.903 4.0007 3.9609 4.0759 4.4619 4.6971 u149 0.9689 0.8698 1.2855 1.8257 2.8561 3.3217 3.67 3.6367 3.9043 4.0206 3.9614 4.0808 4.4596 4.6973 u150 0.9687 0.87 1.2859 1.8262 2.8571 3.3218 3.67 3.6452 3.8438 3.9803 3.9427 4.0847 4.4669 4.7021 u151 0.9684 0.8701 1.2862 1.8262 2.8578 3.3218 3.67 3.6295 3.8431 3.9605 3.9422 4.0797 4.4695 4.7021 u152 0.9691 0.8723 1.2893 1.8298 2.8634 3.3273 3.6712 3.8836 3.9958 3.7909 3.8355 4.0579 4.4795 4.7184 u153 0.9688 0.8723 1.2894 1.8301 2.8644 3.327 3.6711 3.9072 3.9979 3.8062 3.8366 4.0627 4.4771 4.7185 u154 0.9683 0.8722 1.2892 1.8299 2.8651 3.3267 3.671 3.894 4.0858 3.8389 3.8507 4.0589 4.4702 4.7137 u155 0.968 0.8722 1.2894 1.8299 2.8656 3.3267 3.671 3.8706 4.0849 3.8218 3.8494 4.0541 4.4728 4.7137 u156 0.9681 0.8728 1.2904 1.831 2.8674 3.3278 3.6713 3.7929 3.8716 3.7359 3.8247 4.0555 4.4893 4.7272 u157 0.9676 0.8728 1.2905 1.8312 2.8685 3.3276 3.6713 3.8145 3.8732 3.7502 3.8258 4.0603 4.4869 4.7272 u158 0.9676 0.873 1.291 1.8317 2.8693 3.3277 3.6714 3.8267 3.8076 3.7206 3.8127 4.0641 4.4939 4.7322 u159 0.9672 0.873 1.2912 1.8318 2.87 3.3278 3.6713 3.8042 3.8069 3.7063 3.8114 4.0594 4.4965 4.7321 u160 0.9727 0.8451 1.2226 1.7395 2.8107 3.2735 3.6744 3.5924 3.6574 3.537 3.7404 4.1904 4.6892 5.1275 u161 0.9718 0.845 1.2227 1.7398 2.8113 3.2734 3.6743 3.6072 3.6579 3.5589 3.741 4.1941 4.6865 5.1268 u162 0.9707 0.8447 1.2227 1.7397 2.8118 3.2731 3.674 3.5983 3.7031 3.5843 3.7505 4.1911 4.6797 5.1194 u163 0.9695 0.8446 1.2228 1.7398 2.8122 3.2732 3.6739 3.5825 3.7017 3.5955 3.7495 4.1876 4.6827 5.12 u164 0.9681 0.844 1.2222 1.7391 2.8119 3.2719 3.6734 3.6386 3.8422 3.6134 3.7683 4.1906 4.6669 5.1022 u165 0.9672 0.8438 1.2225 1.7394 2.8124 3.2718 3.6733 3.6537 3.8425 3.6259 3.7692 4.1945 4.6642 5.1016 u166 0.9663 0.8439 1.223 1.7398 2.8132 3.272 3.6733 3.6616 3.7867 3.6118 3.7599 4.1979 4.6713 5.1088 u167 0.9654 0.8438 1.2232 1.7399 2.8137 3.2721 3.6732 3.6453 3.7849 3.6075 3.7589 4.1941 4.6744 5.1094 u168 0.9625 0.8415 1.2207 1.737 2.8096 3.2668 3.6714 3.5033 3.6841 3.7328 3.8276 4.222 4.6693 5.0925 u169 0.9619 0.8414 1.2209 1.7373 2.8101 3.2667 3.6712 3.5032 3.6846 3.7442 3.8283 4.2259 4.6664 5.0919 u170 0.9603 0.841 1.2208 1.7372 2.8104 3.2665 3.671 3.4823 3.7277 3.7691 3.8393 4.2224 4.6593 5.0845 u171 0.9596 0.8409 1.221 1.7373 2.8108 3.2666 3.6709 3.4601 3.7263 3.7556 3.8386 4.2184 4.6623 5.085 u172 0.9589 0.8413 1.2221 1.7383 2.8126 3.2678 3.6712 3.395 3.6148 3.6824 3.8182 4.2152 4.6787 5.1031 u173 0.9578 0.8412 1.2222 1.7385 2.8131 3.2677 3.6711 3.393 3.6153 3.6948 3.8189 4.2191 4.6759 5.1025 u174 0.957 0.8412 1.2228 1.739 2.8138 3.268 3.6711 3.3876 3.5805 3.6706 3.8085 4.2226 4.6832 5.1099 u175 0.9556 0.841 1.2229 1.7392 2.8142 3.2681 3.671 3.3623 3.5802 3.6585 3.8076 4.2186 4.6863 5.1105 u176 0.9631 0.851 1.2363 1.7547 2.8429 3.2876 3.6765 3.5774 3.7135 3.8241 3.6999 4.0963 4.5241 5.0255 u177 0.9621 0.8509 1.2364 1.7549 2.8433 3.2875 3.6763 3.5919 3.7142 3.8394 3.7007 4.1008 4.5217 5.025 u178 0.9609 0.8506 1.2363 1.7548 2.8437 3.2872 3.6761 3.5841 3.766 3.8729 3.7093 4.0972 4.5148 5.0184 u179 0.9601 0.8505 1.2365 1.7548 2.8443 3.2873 3.6761 3.5699 3.7649 3.8551 3.708 4.0927 4.5175 5.0187 u180 0.9585 0.8499 1.236 1.7542 2.8435 3.2861 3.6755 3.6241 3.9263 3.9567 3.725 4.0931 4.5009 5.0022 u181 0.9574 0.8497 1.236 1.7544 2.8442 3.286 3.6754 3.6389 3.9272 3.9768 3.7259 4.0978 4.4985 5.0017 u182 0.9566 0.8498 1.2366 1.7549 2.8449 3.2862 3.6754 3.6472 3.8634 3.9368 3.7168 4.1015 4.5058 5.0082 u183 0.9556 0.8497 1.2368 1.755 2.8455 3.2863 3.6754 3.6322 3.8621 3.9175 3.7152 4.0969 4.5084 5.0084 u184 0.9566 0.8518 1.2398 1.7583 2.8508 3.2917 3.6769 3.8911 4.0272 3.7501 3.6486 4.0746 4.517 5.0256 u185 0.9555 0.8517 1.2399 1.7585 2.8515 3.2915 3.6768 3.9152 4.0282 3.7628 3.6507 4.0795 4.5146 5.0251 u186 0.9545 0.8514 1.2398 1.7584 2.8517 3.2913 3.6766 3.9028 4.1171 3.791 3.66 4.0762 4.5077 5.0186 u187 0.9533 0.8512 1.2399 1.7585 2.8521 3.2914 3.6765 3.8799 4.1151 3.7732 3.6593 4.0718 4.5102 5.0189 u188 0.9529 0.8517 1.241 1.7596 2.8539 3.2926 3.6769 3.8042 3.8951 3.6937 3.6446 4.073 4.526 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7.0226 12.0464 12.7787 u25 2.926 2.9883 2.998 3.016 3.2012 6.3649 6.8445 6.9821 7.006 7.0162 7.0236 12.0451 12.7739 u26 2.926 2.9876 2.9977 3.0164 3.2021 6.3652 6.8449 6.9834 7.0068 7.0172 7.0225 12.046 12.796 u27 2.9261 2.9877 2.9977 3.0166 3.2017 6.3654 6.8439 6.9832 7.0068 7.0185 7.0221 12.0459 12.7936 u28 2.9254 2.9869 2.9972 3.0169 3.2021 6.3656 6.8436 6.9843 7.0066 7.0174 7.0583 13.7568 14.7454 u29 2.9255 2.9867 2.9972 3.0166 3.2025 6.3655 6.8436 6.9836 7.0071 7.0171 7.0593 13.755 14.7321 u30 2.9256 2.9872 2.9977 3.016 3.2019 6.3654 6.8441 6.9831 7.0056 7.0164 7.0606 13.7554 14.7533 u31 2.9255 2.9873 2.9978 3.0158 3.2012 6.3645 6.8445 6.9836 7.0053 7.0167 7.0596 13.7551 14.742 u32 4.943 5.0066 5.0138 5.0267 5.1163 8.3693 8.8596 9.005 9.0251 9.0365 9.0268 15.7582 16.7635 u33 4.9428 5.0067 5.0142 5.0261 5.1169 8.3694 8.8581 9.005 9.0227 9.0368 9.0258 15.7574 16.7563 u34 4.9428 5.0069 5.0143 5.0257 5.1163 8.3694 8.8589 9.0053 9.0215 9.0349 9.0251 15.7583 16.7781 u35 4.9431 5.0066 5.0141 5.026 5.1154 8.3699 8.8593 9.0053 9.0232 9.0372 9.0266 15.7578 16.8022 u36 4.9429 5.0065 5.0143 5.0264 5.1165 8.3701 8.859 9.0057 9.023 9.0355 9.1026 17.4856 18.756 u37 4.943 5.0067 5.0146 5.0259 5.1169 8.3688 8.8579 9.0058 9.0213 9.0357 9.1029 17.4872 18.7621 u38 4.9431 5.0064 5.0144 5.0263 5.1176 8.3691 8.8581 9.0061 9.0232 9.0361 9.1028 17.4879 18.7421 u39 4.9431 5.0063 5.0141 5.0265 5.1171 8.3698 8.8589 9.0058 9.0244 9.0362 9.1028 17.4864 18.7824 u40 4.9434 5.007 5.0146 5.0464 5.3808 10.1049 10.8109 11.0209 11.0452 11.0631 11.0233 19.4901 20.7983 u41 4.9431 5.0072 5.0148 5.0458 5.3821 10.1052 10.8111 11.0207 11.0469 11.0636 11.0241 19.4896 20.8081 u42 4.943 5.0074 5.0147 5.0458 5.3819 10.1043 10.8111 11.0201 11.0477 11.0623 11.0245 19.4909 20.7991 u43 4.9432 5.0072 5.0145 5.0461 5.3807 10.106 10.8102 11.0201 11.0455 11.062 11.0235 19.4897 20.8173 u44 4.9427 5.0075 5.0136 5.0456 5.3798 10.1054 10.8103 11.0208 11.0452 11.0615 11.1787 21.2453 22.758 u45 4.9428 5.0076 5.014 5.0453 5.3808 10.1043 10.8108 11.0209 11.0477 11.0619 11.1793 21.245 22.7904 u46 4.943 5.0072 5.0141 5.0453 5.3812 10.1046 10.8112 11.0214 11.0474 11.0617 11.1788 21.244 22.7842 u47 4.9429 5.0069 5.0139 5.0459 5.38 10.1056 10.811 11.0213 11.0442 11.0629 11.1783 21.2443 22.7874 u48 6.9184 7.035 7.0489 7.0528 7.18 12.1168 12.8458 13.0654 13.0877 13.098 13.0171 23.2538 24.7711 u49 6.9183 7.0347 7.0485 7.0536 7.1793 12.1183 12.8454 13.066 13.0859 13.0988 13.0178 23.2544 24.8001 u50 6.918 7.0349 7.0482 7.0535 7.1794 12.1185 12.8458 13.0655 13.0853 13.0992 13.018 23.2522 24.8226 u51 6.9182 7.035 7.0487 7.053 7.1801 12.1168 12.8459 13.0656 13.0871 13.0994 13.0168 23.2528 24.8065 u52 6.918 7.0349 7.0485 7.0531 7.1795 12.1169 12.8459 13.0656 13.087 13.1016 13.317 25.0373 26.7414 u53 6.9178 7.0346 7.0479 7.0533 7.1787 12.1181 12.8463 13.0653 13.0856 13.1012 13.317 25.0387 26.7576 u54 6.918 7.0343 7.0484 7.0533 7.179 12.1169 12.8458 13.0657 13.0865 13.1 13.3165 25.0376 26.7502 u55 6.9181 7.0344 7.0489 7.0531 7.1796 12.1159 12.8459 13.0654 13.0882 13.1006 13.3156 25.037 26.7618 u56 6.9179 7.0351 7.0525 7.102 7.6835 13.912 14.836 15.1121 15.1389 15.1479 15.0352 27.0541 28.7752 u57 6.9178 7.0349 7.052 7.1025 7.6829 13.913 14.8349 15.1121 15.1387 15.1479 15.0335 27.0545 28.7672 u58 6.9175 7.0351 7.0515 7.1026 7.6827 13.911 14.836 15.1126 15.1396 15.1466 15.0335 27.0547 28.8046 u59 6.9176 7.0352 7.052 7.102 7.6833 13.9101 14.8368 15.1125 15.1403 15.1473 15.0337 27.0524 28.7706 u60 6.9176 7.0355 7.0517 7.1019 7.6838 13.9096 14.8368 15.1121 15.1403 15.1524 15.5652 28.8737 30.7564 u61 6.9175 7.0352 7.0512 7.1023 7.6832 13.9096 14.8358 15.1124 15.1406 15.1522 15.5659 28.8742 30.762 u62 6.9178 7.0349 7.0518 7.1021 7.6834 13.9106 14.8361 15.1119 15.1401 15.1533 15.5665 28.8733 30.774 u63 6.9179 7.0349 7.0525 7.1015 7.684 13.9105 14.8364 15.1119 15.1387 15.1538 15.5656 28.8728 30.7724 u64 8.9889 9.1124 9.1154 9.0905 9.3435 15.939 16.9028 17.1925 17.2145 17.2075 17.1515 30.8997 32.8382 u65 8.989 9.1124 9.1155 9.09 9.3429 15.9401 16.9024 17.192 17.2135 17.2078 17.1513 30.897 32.834 u66 8.989 9.1125 9.1154 9.0887 9.3429 15.9396 16.9015 17.1922 17.2131 17.2089 17.1513 30.898 32.8385 u67 8.9889 9.1124 9.1154 9.0894 9.3422 15.9389 16.9016 17.1924 17.2135 17.2108 17.1519 30.9004 32.8425 u68 8.9888 9.1115 9.1153 9.0893 9.3432 15.9391 16.902 17.1913 17.2136 17.224 17.9625 32.7536 34.8915 u69 8.989 9.1116 9.1153 9.0883 9.3445 15.9387 16.9021 17.1917 17.2133 17.2239 17.9625 32.754 34.9238 u70 8.989 9.1113 9.1155 9.0894 9.3428 15.9393 16.9031 17.1917 17.2128 17.2219 17.9618 32.7537 34.9064 u71 8.9888 9.1112 9.1154 9.0901 9.3422 15.9397 16.9029 17.1919 17.2141 17.2218 17.9621 32.7539 34.8983 u72 8.9883 9.1126 9.1278 9.2152 10.1727 17.8043 18.9416 19.284 19.3025 19.2838 19.4368 34.7917 37.0328 u73 8.9883 9.1127 9.1278 9.2144 10.1728 17.8043 18.9422 19.2843 19.3034 19.2823 19.4362 34.7938 37.0074 u74 8.9883 9.1128 9.1275 9.2134 10.1728 17.8046 18.9422 19.2835 19.3034 19.2808 19.4366 34.7931 37.049 u75 8.9883 9.1126 9.1274 9.214 10.1726 17.804 18.9418 19.2838 19.3031 19.2822 19.4366 34.7921 37.0498 u76 8.9879 9.1136 9.127 9.2139 10.1717 17.8043 18.9408 19.283 19.3045 19.3161 20.4608 36.6833 39.1338 u77 8.9882 9.1135 9.1271 9.2133 10.1715 17.8034 18.9414 19.2829 19.3053 19.3159 20.4601 36.6848 39.1318 u78 8.9882 9.1132 9.1274 9.2141 10.1715 17.8037 18.9416 19.2832 19.3039 19.3173 20.4615 36.6846 39.1573 u79 8.9879 9.113 9.1276 9.2149 10.1715 17.8046 18.9412 19.2829 19.3044 19.3177 20.4603 36.6855 39.1485 u80 11.0636 11.2257 11.2138 11.1333 11.7119 19.8603 21.0509 21.4132 21.4179 21.3639 21.8706 38.7381 41.2799 u81 11.0635 11.2255 11.2144 11.133 11.7116 19.8599 21.0506 21.4127 21.4183 21.3649 21.8712 38.7377 41.274 u82 11.0637 11.2257 11.2154 11.1333 11.714 19.8602 21.0514 21.412 21.4187 21.367 21.8696 38.7374 41.2822 u83 11.0639 11.2255 11.2149 11.1333 11.7117 19.8611 21.0516 21.4124 21.4181 21.3652 21.8704 38.7382 41.2946 u84 11.0636 11.2256 11.2147 11.1325 11.7111 19.8606 21.0519 21.412 21.4196 21.4457 23.0163 40.6713 43.3561 u85 11.0637 11.2254 11.2151 11.1323 11.7113 19.8594 21.0518 21.4115 21.4193 21.4475 23.0154 40.6708 43.3658 u86 11.0636 11.2251 11.2143 11.1324 11.7106 19.8593 21.0512 21.4123 21.4197 21.4453 23.0154 40.669 43.3851 u87 11.0634 11.2251 11.2137 11.132 11.714 19.8607 21.0514 21.4125 21.4195 21.4441 23.0154 40.6703 43.3788 u88 11.0635 11.2303 11.255 11.4297 12.8247 21.8089 23.1564 23.5631 23.5565 23.4484 24.4043 42.7415 45.4971 u89 11.0633 11.2301 11.2554 11.4297 12.8245 21.8089 23.1564 23.5628 23.5571 23.4487 24.4032 42.7419 45.4756 u90 11.0633 11.2303 11.2562 11.4299 12.8252 21.8093 23.1561 23.5638 23.5551 23.4475 24.4028 42.7419 45.5104 u91 11.0634 11.2305 11.2557 11.4301 12.8255 21.8085 23.1563 23.5634 23.5551 23.4477 24.4038 42.7423 45.5011 u92 11.0627 11.2306 11.2554 11.4311 12.8253 21.8092 23.1564 23.5634 23.5585 23.6271 25.6147 44.7195 47.5966 u93 11.063 11.2304 11.2559 11.4304 12.825 21.8076 23.1563 23.5634 23.5585 23.6292 25.6146 44.7194 47.5794 u94 11.0631 11.23 11.2552 11.4304 12.8244 21.8081 23.1568 23.5627 23.5601 23.63 25.6146 44.7185 47.5895 u95 11.063 11.23 11.2548 11.4308 12.8248 21.8085 23.1569 23.5624 23.5605 23.6289 25.6147 44.7188 47.6034 u96 13.238 13.4045 13.3474 13.2218 14.3021 23.9092 25.3244 25.7523 25.7204 25.5373 27.0007 46.8185 49.7372 u97 13.2379 13.4042 13.3472 13.2221 14.3023 23.9098 25.3243 25.7529 25.7207 25.5368 27.0028 46.8174 49.7333 u98 13.2383 13.404 13.3474 13.2222 14.3029 23.9092 25.3255 25.7533 25.7214 25.5382 27.0018 46.8156 49.7527 u99 13.2385 13.4039 13.3477 13.2222 14.3012 23.9103 25.3258 25.7523 25.7213 25.5391 27.0024 46.817 49.7679 u100 13.2378 13.4047 13.3472 13.2224 14.3027 23.9087 25.3249 25.7531 25.734 25.9116 28.2609 48.8416 51.9278 u101 13.2378 13.4046 13.3469 13.222 14.3024 23.9092 25.3248 25.7536 25.734 25.9119 28.2599 48.8413 51.9214 u102 13.2375 13.4047 13.3468 13.2221 14.302 23.9096 25.324 25.7535 25.7331 25.9103 28.2605 48.8403 51.9044 u103 13.2375 13.4048 13.3471 13.2225 14.3015 23.91 25.3242 25.7524 25.7325 25.9106 28.2616 48.8409 51.9312 u104 13.2391 13.4233 13.4684 13.8408 15.5915 25.9553 27.5089 27.9747 27.9107 27.6829 29.6585 50.9665 54.1339 u105 13.2389 13.4231 13.4682 13.8403 15.5907 25.9553 27.5085 27.9736 27.9119 27.6841 29.6577 50.9665 54.1353 u106 13.239 13.4228 13.4683 13.8398 15.5901 25.9561 27.5075 27.9729 27.912 27.6833 29.6589 50.9668 54.1497 u107 13.2392 13.4229 13.4688 13.8403 15.5904 25.9557 27.5079 27.9735 27.9103 27.6833 29.658 50.9656 54.153 u108 13.2393 13.4222 13.4685 13.8404 15.5907 25.9561 27.5071 27.9737 27.9447 28.3612 30.9625 53.0371 56.3735 u109 13.2393 13.4219 13.4683 13.8397 15.59 25.9555 27.5069 27.9728 27.9449 28.3617 30.9625 53.0375 56.3731 u110 13.2391 13.422 13.4684 13.8401 15.5907 25.9546 27.5083 27.9736 27.9445 28.3619 30.9619 53.0392 56.3708 u111 13.2392 13.422 13.4686 13.8405 15.5915 25.9555 27.5086 27.9746 27.9429 28.3611 30.9626 53.0367 56.3715 u112 15.4682 15.6379 15.5055 15.4971 17.0655 28.1189 29.7544 30.2383 30.1253 29.9964 32.377 55.1971 58.6171 u113 15.468 15.6378 15.5053 15.4946 17.066 28.1209 29.7553 30.2392 30.1233 29.9954 32.3779 55.1981 58.6306 u114 15.4686 15.6374 15.5057 15.4942 17.0666 28.1201 29.7563 30.2425 30.1228 29.9966 32.3777 55.1972 58.6651 u115 15.4691 15.6373 15.506 15.4947 17.0661 28.1177 29.7553 30.2416 30.1244 29.9972 32.3781 55.1962 58.6498 u116 15.468 15.6383 15.5056 15.4943 17.0656 28.1195 29.7554 30.2423 30.2081 30.9996 33.727 57.3247 60.9064 u117 15.4683 15.6382 15.5053 15.4973 17.0666 28.121 29.7563 30.2431 30.206 31.0002 33.7268 57.3256 60.9193 u118 15.4684 15.6384 15.505 15.4951 17.0657 28.1213 29.7559 30.2397 30.2067 31.0002 33.7276 57.326 60.9137 u119 15.4682 15.6383 15.5053 15.4945 17.0656 28.1197 29.7547 30.2385 30.2086 30.9994 33.7265 57.3265 60.913 u120 15.48 15.7077 15.8267 16.5167 18.4674 30.2759 32.0361 32.5546 32.346 32.5328 35.1644 59.531 63.2167 u121 15.4799 15.7078 15.8268 16.5166 18.4668 30.2747 32.0366 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18.1475 18.4517 19.3938 21.4901 34.8137 36.7837 37.2781 37.7322 39.5062 42.4347 70.8714 75.1479 u141 17.8571 18.1476 18.4523 19.3938 21.4906 34.8127 36.7834 37.2769 37.7329 39.5069 42.4361 70.872 75.1592 u142 17.8576 18.1479 18.4516 19.3933 21.4906 34.8145 36.79 37.3706 37.7332 39.5058 42.4355 70.871 75.1566 u143 17.8572 18.1478 18.4511 19.393 21.4902 34.8145 36.7897 37.3711 37.7305 39.5061 42.4359 70.8711 75.1594 u144 20.2164 20.2868 20.2349 20.9428 23.0809 37.1945 39.2538 39.6865 39.482 41.0327 43.9712 73.252 77.6014 u145 20.2164 20.287 20.2356 20.9426 23.0807 37.195 39.2526 39.6866 39.4816 41.034 43.9718 73.2505 77.6106 u146 20.2171 20.2869 20.2342 20.9421 23.0807 37.1962 39.274 39.9285 39.4807 41.0336 43.9717 73.2474 77.6082 u147 20.2176 20.2868 20.2369 20.9427 23.0813 37.1952 39.2746 39.9281 39.4814 41.0328 43.9714 73.2497 77.6298 u148 20.217 20.2859 20.237 20.9425 23.081 37.1956 39.2739 39.9286 40.6736 42.5141 45.5107 75.6539 80.0702 u149 20.2176 20.286 20.2346 20.9428 23.0802 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45.6272 48.6948 80.6023 85.2642 u159 20.4136 20.8596 21.4451 22.4465 24.7003 39.645 41.8455 42.6806 43.756 45.628 48.6943 80.603 85.2381 u160 22.7291 22.8715 23.1502 24.0705 26.3971 42.1758 44.3495 44.7258 45.4031 47.2433 50.3384 83.1437 87.8673 u161 22.7294 22.8727 23.1507 24.0704 26.3968 42.1757 44.3493 44.7254 45.4024 47.243 50.338 83.1448 87.8502 u162 22.73 22.8707 23.1507 24.0708 26.3974 42.1754 44.5584 45.741 45.402 47.2432 50.3384 83.1435 87.8769 u163 22.7298 22.8702 23.1508 24.0713 26.3978 42.1756 44.558 45.7422 45.4029 47.2445 50.337 83.1439 87.8927 u164 22.7288 22.8717 23.1507 24.0707 26.4013 42.203 44.5579 45.7394 46.9637 48.8623 52.004 85.7289 90.4885 u165 22.7295 22.8715 23.1507 24.0709 26.4009 42.2038 44.5571 45.7419 46.9648 48.8638 52.0058 85.7305 90.5115 u166 22.729 22.8707 23.1498 24.0699 26.4004 42.2042 44.349 44.7255 46.9632 48.8622 52.0053 85.7292 90.5583 u167 22.7284 22.8704 23.1502 24.0703 26.4008 42.2038 44.3487 44.7263 46.9632 48.8632 52.0037 85.7283 90.5501 u168 23.3002 24.0312 24.7181 25.7297 28.1493 44.7811 47.4893 49.0867 48.6496 50.5432 53.7116 88.3704 93.1711 u169 23.3003 24.0317 24.7177 25.7301 28.149 44.7822 47.4905 49.0874 48.6492 50.5421 53.7115 88.3729 93.1834 u170 23.3001 24.0319 24.7176 25.73 28.1485 44.7836 46.9655 47.6436 48.6506 50.5416 53.7107 88.375 93.3431 u171 23.3002 24.0318 24.7178 25.7296 28.1488 44.7825 46.9643 47.6417 48.6501 50.543 53.7117 88.3731 93.3278 u172 23.2994 24.0301 24.7179 25.7324 28.1662 44.884 46.9645 47.6414 50.3142 52.2443 55.4501 91.0631 95.8755 u173 23.2995 24.0303 24.7179 25.7328 28.1658 44.8843 46.9654 47.6423 50.3159 52.2445 55.4497 91.0624 95.8431 u174 23.2997 24.0301 24.7179 25.7328 28.1663 44.8817 47.4898 49.087 50.3149 52.244 55.4498 91.0797 96.2453 u175 23.2996 24.0299 24.7182 25.7325 28.1669 44.8822 47.4881 49.0874 50.3157 52.244 55.4507 91.0806 96.2669 u176 25.5008 25.9515 26.4839 27.4846 29.9714 47.4569 49.7368 50.924 52.068 54 57.23 93.8035 98.5959 u177 25.5014 25.9515 26.4825 27.4846 29.9715 47.4576 49.7351 50.9237 52.0678 54 57.2336 93.8015 98.626 u178 25.5017 25.9508 26.4844 27.4846 29.9714 47.4561 50.7927 52.6194 52.0687 54.0003 57.2363 93.8651 99.3573 u179 25.5017 25.9514 26.4829 27.4847 29.9713 47.456 50.7912 52.6204 52.0688 54.0007 57.2322 93.8657 99.3658 u180 25.5014 25.9516 26.4861 27.5004 30.0364 47.7567 50.7908 52.6186 53.8366 55.7934 59.0631 96.5768 101.5264 u181 25.5028 25.9505 26.4855 27.5001 30.0362 47.7543 50.792 52.6204 53.8379 55.7949 59.0487 96.5759 101.5192 u182 25.503 25.9503 26.4853 27.5 30.0364 47.7547 49.7345 50.9223 53.8375 55.7947 59.0513 96.744 102.7774 u183 25.5017 25.9503 26.4848 27.5001 30.0366 47.756 49.7351 50.923 53.8375 55.7945 59.0654 96.7471 102.758 u184 26.7564 27.6499 28.2924 29.3043 31.8445 50.2126 54.481 56.352 55.6799 57.6402 60.9066 99.3737 104.7895 u185 26.7557 27.6505 28.2926 29.3046 31.8444 50.2112 54.482 56.3524 55.6794 57.6402 60.9514 99.3735 104.784 u186 26.756 27.6502 28.2928 29.3051 31.845 50.2115 52.8879 54.4937 55.6799 57.6424 60.9527 99.7791 106.3724 u187 26.7572 27.6495 28.2926 29.3047 31.8451 50.2119 52.8889 54.4927 55.6801 57.6445 60.9074 99.7778 106.3917 u188 26.7547 27.6507 28.3062 29.37 32.0502 50.946 52.8873 54.4931 57.5635 59.5304 62.9105 102.2392 108.3364 u189 26.7551 27.6515 28.3063 29.3703 32.0499 50.9478 52.8862 54.4933 57.5626 59.53 62.7907 102.2389 108.3192 u190 26.7555 27.6518 28.3063 29.3699 32.0493 50.9473 54.4811 56.3535 57.5625 59.5426 62.7919 103.0672 110.0782 u191 26.7557 27.6508 28.3063 29.3696 32.0496 50.9471 54.4777 56.3517 57.5619 59.5421 62.9118 103.0709 110.098 u192 28.8967 29.6329 30.2211 31.1985 33.7878 53.2472 56.5129 58.3201 59.5158 61.4692 64.6982 105.3423 112.0229 u193 28.8954 29.6343 30.221 31.1988 33.7878 53.2474 56.5126 58.3198 59.515 61.47 64.9878 105.3399 112.0215 u194 28.8984 29.6333 30.2209 31.1977 33.7875 53.2471 58.4305 60.3284 59.518 61.5083 64.9887 106.6962 113.9226 u195 28.8957 29.6335 30.2207 31.1976 33.788 53.2469 58.432 60.3294 59.5174 61.51 64.6986 106.6951 113.9457 u196 28.8964 29.6482 30.2886 31.4137 34.3072 54.6317 58.4322 60.3288 61.5225 63.4448 67.26 108.8201 115.9569 u197 28.8963 29.6491 30.2889 31.4126 34.306 54.6309 58.4293 60.3278 61.5228 63.4457 66.6604 108.8239 115.9373 u198 28.894 29.6479 30.289 31.4145 34.3064 54.6318 56.5113 58.3212 61.5361 63.5607 66.6623 110.5569 117.9697 u199 28.8976 29.6487 30.2896 31.4154 34.3076 54.6318 56.5111 58.321 61.5357 63.5603 67.2615 110.5568 117.968 u200 30.8385 31.6761 32.2269 33.1745 35.9425 56.8147 62.6807 64.6275 63.5938 65.4511 68.8078 112.6399 120.0732 u201 30.8381 31.6768 32.2268 33.1746 35.9421 56.8143 62.6818 64.6076 63.5943 65.4502 69.7793 112.6406 120.0877 u202 30.8377 31.6763 32.227 33.1739 35.9427 56.8128 60.5371 62.4377 63.6434 65.7446 69.7799 114.58 122.2273 u203 30.8383 31.676 32.2271 33.1741 35.9422 56.8135 60.5377 62.4326 63.6414 65.7458 68.808 114.5829 122.2176 u204 30.8669 31.7659 32.4737 33.7422 36.9479 58.7337 60.5375 62.4332 65.7106 67.522 72.4667 116.7006 124.3592 u205 30.8648 31.7665 32.4732 33.7425 36.9485 58.7335 60.5371 62.4378 65.711 67.5211 71.2356 116.7014 124.3665 u206 30.864 31.767 32.4725 33.7413 36.9488 58.7342 62.6812 64.6057 65.8604 68.1558 71.236 118.7805 126.5951 u207 30.8655 31.7664 32.473 33.7407 36.9481 58.7348 62.6782 64.6256 65.861 68.1547 72.4679 118.7799 126.6084 u208 33.0856 33.8573 34.3557 35.4122 38.511 60.9485 64.961 66.8665 67.8719 69.8016 73.9063 120.9783 128.8537 u209 33.0853 33.8583 34.3563 35.4118 38.5104 60.9502 64.9502 66.9393 67.8724 69.8028 75.282 120.979 128.8255 u210 33.0852 33.8597 34.3549 35.4117 38.5094 60.9512 67.3556 69.1826 68.2597 70.8585 75.2825 123.1866 131.1588 u211 33.0862 33.8583 34.356 35.411 38.5111 60.9498 67.3087 69.4073 68.2601 70.8586 73.9069 123.1854 131.1615 u212 33.2214 34.1824 35.0169 36.5131 39.9201 63.2019 67.3081 69.4075 70.1446 72.4123 78.2505 125.4882 133.5366 u213 33.2217 34.1828 35.0176 36.5134 39.9208 63.1955 67.355 69.1817 70.1445 72.4125 76.7655 125.4847 133.5237 u214 33.2237 34.1822 35.0165 36.5124 39.9194 63.1964 64.9502 66.9385 70.956 73.7621 76.7652 127.8281 136.0317 u215 33.2235 34.1819 35.0172 36.5121 39.9192 63.2003 64.9603 66.8654 70.9565 73.7626 78.2503 127.8291 136.0114 u216 35.445 36.2138 36.8228 38.1341 41.5374 65.6006 72.2936 75.2914 72.7133 75.3159 79.8088 130.2594 138.5627 u217 35.4434 36.2154 36.823 38.134 41.5384 65.6352 72.7658 74.1616 72.7133 75.3153 81.3985 130.2599 138.5417 u218 35.443 36.2148 36.8226 38.1337 41.5337 65.635 69.7645 72.1447 73.9916 76.8318 81.398 132.7503 141.24 u219 35.4452 36.2154 36.822 38.1335 41.5332 65.6034 69.9292 71.5687 73.9915 76.8334 79.8097 132.7523 141.1228 u220 35.9446 37.0809 38.1143 39.6668 43.2259 68.2437 69.93 71.5669 75.6828 78.4548 84.7489 135.3208 143.9764 u221 35.9439 37.0807 38.1159 39.6739 43.2253 68.1096 69.7646 72.1413 75.6824 78.4533 83.05 135.3322 143.7174 u222 35.9415 37.0793 38.1138 39.6751 43.1935 68.1097 72.7645 74.1629 77.2562 80.1038 83.0502 137.9532 146.9884 u223 35.9399 37.0795 38.1142 39.6685 43.1934 68.2451 72.2929 75.2906 77.2558 80.1025 84.7445 138.0018 146.3707 u224 38.1421 39.0748 39.9061 41.4312 45.0921 70.724 76.0497 77.1971 78.9949 81.8321 86.5172 140.6489 150.2997 u225 38.1407 39.0737 39.9051 41.3874 45.0917 71.148 75.0027 78.8149 78.9935 81.8308 88.3057 140.7959 149.1778 u226 38.1387 39.0729 39.9136 41.3874 44.9563 71.1475 79.8563 80.725 80.7524 83.6178 88.3586 143.3857 153.9366 u227 38.1393 39.072 39.9138 41.4318 44.9577 70.7252 78.1693 82.6313 80.752 83.6106 86.5021 143.7715 152.3383 u228 39.3811 40.6933 41.6807 43.1806 47.2136 74.5365 78.1688 82.6346 82.615 85.4919 92.4479 146.2133 157.7208 u229 39.3797 40.6954 41.6813 43.3578 47.2147 73.5145 79.8549 80.7237 82.6175 85.4642 90.1531 147.0624 155.918 u230 39.383 40.7177 41.7473 43.3615 46.7928 73.5134 75.0026 78.8136 84.5431 87.468 90.3172 149.3221 161.6712 u231 39.3822 40.7174 41.7472 43.1824 46.7917 74.5368 76.0486 77.1971 84.5564 87.3728 92.0413 150.7556 159.7367 u232 41.5864 42.737 43.629 45.6178 49.8016 76.7947 86.3111 91.7814 86.5573 89.6002 94.8545 152.8896 165.8723 u233 41.5862 42.7351 43.6295 45.0949 49.7866 78.5611 88.8104 89.0424 86.6142 89.3315 96.3559 154.7376 163.7698 u234 41.6242 42.8512 43.8894 45.0964 48.8317 78.5612 81.9544 86.8512 88.6314 91.9867 97.5297 156.866 170.3772 u235 41.6217 42.8509 43.8899 45.6189 48.8326 76.7942 84.0476 84.681 88.8158 91.3653 94.0545 158.9374 168.0686 u236 43.6586 44.8534 45.73 47.2945 56.2922 83.0754 84.0414 84.6904 90.773 94.7231 103.4371 161.1551 175.1357 u237 43.6584 44.8547 45.7322 48.4058 55.1603 80.8156 81.9552 86.8115 91.2635 93.6365 98.9928 163.3988 172.7418 u238 43.91 45.3023 46.474 48.4076 51.4219 80.8115 88.6749 89.1885 93.1011 97.712 100.3833 165.7558 180.196 u239 43.9111 45.3011 46.474 47.2943 51.4466 83.1093 86.3407 91.3499 94.1018 96.2886 101.9016 168.1813 177.6286 u240 46.0819 47.3076 48.295 51.6846 52.6019 85.527 93.8045 94.7999 95.8386 103.2027 106.7386 170.7183 185.5392 u241 46.0848 47.3029 48.2917 50.0756 53.0145 88.5886 91.5754 96.7404 97.3072 99.3683 108.4985 173.352 182.8435 u242 46.875 48.4368 49.7504 50.0677 54.5156 88.0935 100.855 102.1953 99.0435 100.7888 110.3385 176.0937 191.2394 u243 46.8669 48.4418 49.7745 51.755 57.1194 85.6786 98.6951 104.3252 100.7888 104.8564 105.0578 178.9503 188.3099 u244 49.0907 50.4654 51.6106 53.482 58.5488 94.3568 96.9609 106.5724 102.6686 106.7538 118.5975 181.9285 201.4817 u245 49.0876 50.5103 51.7362 56.187 59.6871 92.0944 103.0735 100.2446 104.6415 113.0328 112.264 185.0249 198.2276 u246 50.8187 52.3785 53.5473 55.4438 61.0587 90.9153 91.1447 98.3088 106.7469 110.8313 114.2781 188.2473 195.0877 u247 50.9711 52.6554 54.014 53.7502 62.383 96.3402 94.8234 93.8297 113.8639 108.735 116.388 191.6011 204.8098 u248 53.1308 54.6369 55.8333 61.0935 63.9382 98.7255 110.9823 109.8671 111.3485 116.2929 128.5722 195.0998 220.3335 u249 53.6727 55.4539 56.9776 59.2965 65.5845 101.2692 108.1322 112.4678 108.9785 124.0975 125.8846 198.7608 208.9816 u250 55.8554 57.4983 58.8538 57.8716 67.4378 104.0613 105.5088 115.268 120.9644 121.3467 123.3387 207.3405 212.6536 u251 57.3141 59.2853 60.7781 63.0654 69.4919 107.1332 114.0763 118.2761 124.0148 118.7481 120.9102 203.3115 216.39 u252 59.7306 61.6024 63.0444 65.3044 71.7827 110.5139 117.4441 121.5172 117.5046 127.78 131.8728 212.2402 229.8116 u253 62.446 64.281 65.6351 67.8256 74.338 114.2433 125.8827 125.0262 127.8356 130.9128 134.9058 216.7609 225.4612 u254 65.7278 67.4355 68.6262 70.6915 77.2123 118.4101 121.8065 128.8876 131.439 134.3281 138.1853 221.6351 235.0857 u255 69.7535 71.2292 72.1775 74.0527 80.5656 123.224 131.1028 133.2942 135.5132 138.1588 141.8506 227.06 240.4439

i) 1048576-QAM/1024-PAM for a Non-Fading Channel

SNR 0 1 2 3 4 5 6 7 8 9 10 u1 1.0002 1 0.9999 0.9999 1.0002 0.9996 1.0001 0.9993 0.9995 1 0.9998 u2 1.0004 1 0.9998 0.9999 1.0005 0.9992 1.0003 0.9982 0.9985 0.9963 0.999 u3 1.0007 1.0001 0.9998 0.9999 1.0007 0.9989 1.0008 0.9992 0.999 0.9959 0.9988 u4 1.0008 1 0.9995 0.9998 1.0009 0.9986 1.001 0.9965 0.9927 0.9921 0.9939 u5 1.0011 1 0.9994 0.9998 1.0011 0.9982 1.002 0.9958 0.9921 0.9921 0.9936 u6 1.0012 1.0001 0.9994 0.9998 1.0014 0.998 1.002 0.9962 0.9929 0.9954 0.994 u7 1.0016 1.0002 0.9993 0.9998 1.0018 0.9978 1.0026 0.9956 0.9937 0.995 0.9938 u8 1.0013 0.9995 0.9986 0.9996 1.0019 0.9974 1.0029 0.9887 0.9727 0.9736 0.9874 u9 1.0015 0.9995 0.9985 0.9995 1.0021 0.997 1.0028 0.9871 0.9721 0.9736 0.9872 u10 1.0018 0.9995 0.9984 0.9994 1.0024 0.9966 1.0031 0.9865 0.9709 0.9698 0.9864 u11 1.002 0.9996 0.9984 0.9994 1.0026 0.9963 1.0037 0.9866 0.9716 0.9695 0.9863 u12 1.0023 0.9998 0.9984 0.9994 1.0029 0.996 1.004 0.9868 0.978 0.9728 0.9908 u13 1.0026 0.9999 0.9983 0.9993 1.0031 0.9957 1.0043 0.9861 0.9771 0.9729 0.9905 u14 1.0028 1 0.9983 0.9993 1.0034 0.9955 1.0041 0.9854 0.9779 0.976 0.9908 u15 1.0031 1.0001 0.9982 0.9993 1.0038 0.9951 1.0047 0.9848 0.9785 0.9756 0.9907 u16 1.0015 0.9972 0.9961 0.9984 1.0033 0.9948 1.0036 1.0275 1.0103 0.941 0.9734 u17 1.0017 0.9972 0.9961 0.9984 1.0036 0.9945 1.0037 1.0268 1.0094 0.9408 0.9732 u18 1.0018 0.9972 0.9959 0.9983 1.0039 0.9943 1.0037 1.0267 1.0085 0.937 0.9727 u19 1.0021 0.9973 0.9958 0.9983 1.0041 0.994 1.0039 1.0274 1.0091 0.9366 0.9728 u20 1.0022 0.9972 0.9956 0.9982 1.0044 0.9938 1.004 1.0261 1.0025 0.9328 0.9683 u21 1.0025 0.9972 0.9955 0.9982 1.0046 0.9934 1.0042 1.0256 1.0018 0.9325 0.9682 u22 1.0027 0.9973 0.9956 0.9982 1.0048 0.9931 1.0043 1.0257 1.0029 0.9355 0.9687 u23 1.003 0.9974 0.9955 0.9981 1.0049 0.993 1.0045 1.0259 1.0035 0.9351 0.9688 u24 1.0037 0.9981 0.9959 0.9983 1.0055 0.9925 1.0051 1.0307 1.0251 0.9552 0.9744 u25 1.0039 0.9982 0.9958 0.9983 1.0057 0.9924 1.0051 1.0299 1.0242 0.955 0.9742 u26 1.004 0.9982 0.9957 0.9982 1.0059 0.992 1.0054 1.0297 1.0232 0.9513 0.9737 u27 1.0044 0.9983 0.9956 0.9981 1.0062 0.9918 1.0051 1.0299 1.0239 0.9507 0.9737 u28 1.0048 0.9985 0.9956 0.9981 1.0065 0.9916 1.0052 1.0306 1.0303 0.9542 0.9779 u29 1.0049 0.9985 0.9956 0.9981 1.0066 0.9912 1.0053 1.0305 1.0297 0.9541 0.9779 u30 1.0052 0.9986 0.9955 0.998 1.0069 0.9909 1.0055 1.0301 1.0306 0.9571 0.9782 u31 1.0055 0.9987 0.9954 0.998 1.0072 0.9908 1.0053 1.0305 1.0313 0.9566 0.9783 u32 0.9979 0.986 0.9856 0.9939 1.0045 0.9905 0.9998 1.0801 1.1118 1.0503 0.9678 u33 0.9982 0.986 0.9856 0.9938 1.0047 0.9903 0.9996 1.0798 1.111 1.0505 0.9677 u34 0.9984 0.986 0.9854 0.9938 1.005 0.99 0.9997 1.0797 1.11 1.0467 0.9671 u35 0.9987 0.9861 0.9853 0.9938 1.0052 0.9898 0.9995 1.0806 1.111 1.0465 0.9671 u36 0.9988 0.986 0.9851 0.9937 1.0056 0.9896 0.9999 1.0795 1.104 1.0425 0.9624 u37 0.999 0.9859 0.9851 0.9936 1.0058 0.9894 0.9999 1.079 1.1033 1.0428 0.9623 u38 0.9992 0.986 0.9851 0.9936 1.006 0.9892 0.9998 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u509 0.9937 0.9872 1.6061 2.3275 2.8575 3.3365 3.6451 7.9113 8.5283 8.2366 9.0581 u510 0.9937 0.9874 1.6061 2.3271 2.8572 3.3368 3.6447 7.9744 8.6705 8.9432 10.01 u511 0.9936 0.9875 1.6059 2.3266 2.8568 3.3373 3.6442 8.1847 8.7834 8.8923 10.2287 SNR 11 12 13 14 15 16 17 18 19 20 u1 0.9999 0.9999 1.0001 0.9999 0.9999 1 1 1 1 1 u2 0.9996 1.0001 1.0002 0.9999 0.9998 1 0.9999 1 1 1.0001 u3 0.9992 1.0001 1.0002 0.9999 0.9998 1 0.9999 1 1 1.0002 u4 0.9977 1.0004 1.001 1 0.9997 0.9999 0.9998 1.0001 1 1.0003 u5 0.9976 1.0004 1.0011 0.9999 0.9996 0.9999 0.9998 1.0001 1 1.0003 u6 0.9973 1.0002 1.0011 0.9999 0.9996 0.9999 0.9998 1 1 1.0004 u7 0.9971 1.0002 1.0011 0.9999 0.9995 0.9999 0.9997 1.0001 1.0001 1.0005 u8 0.9915 1.0004 1.0021 1.0004 0.9993 0.9996 0.9993 0.9998 0.9999 1.0006 u9 0.9915 1.0003 1.0022 1.0004 0.9992 0.9996 0.9993 0.9998 0.9999 1.0006 u10 0.9915 1.0005 1.0023 1.0003 0.9991 0.9996 0.9992 0.9999 0.9999 1.0007 u11 0.9912 1.0006 1.0023 1.0003 0.999 0.9996 0.9992 0.9999 1 1.0007 u12 0.9924 1.0003 1.0017 1.0002 0.9989 0.9996 0.9993 0.9998 1 1.0008 u13 0.9924 1.0003 1.0018 1.0001 0.9989 0.9996 0.9992 0.9998 1 1.0009 u14 0.9922 1.0001 1.0018 1.0001 0.9988 0.9996 0.9992 0.9998 1 1.0009 u15 0.9919 1.0001 1.0018 1.0001 0.9987 0.9995 0.9992 0.9999 1 1.001 u16 0.9848 0.9973 1.0025 1.0014 0.9989 0.9989 0.9989 1 0.9997 1.0008 u17 0.9851 0.9973 1.0026 1.0014 0.9988 0.9989 0.9989 1 0.9997 1.0009 u18 0.9852 0.9975 1.0027 1.0013 0.9987 0.9989 0.9988 1.0001 0.9997 1.0009 u19 0.9852 0.9975 1.0027 1.0013 0.9986 0.9989 0.9988 1.0001 0.9997 1.001 u20 0.9842 0.9977 1.0035 1.0014 0.9986 0.9988 0.9987 1.0001 0.9997 1.001 u21 0.9844 0.9976 1.0035 1.0013 0.9985 0.9988 0.9987 1.0002 0.9997 1.0011 u22 0.9846 0.9973 1.0036 1.0013 0.9985 0.9988 0.9987 1.0002 0.9997 1.0011 u23 0.9847 0.9974 1.0036 1.0013 0.9984 0.9988 0.9987 1.0002 0.9997 1.0011 u24 0.9887 0.9973 1.0027 1.0008 0.9984 0.999 0.9991 1.0004 0.9999 1.0011 u25 0.9886 0.9972 1.0028 1.0007 0.9984 0.999 0.9991 1.0004 0.9999 1.0011 u26 0.9887 0.9974 1.0028 1.0007 0.9983 0.9989 0.999 1.0005 0.9999 1.0011 u27 0.9886 0.9974 1.0028 1.0007 0.9982 0.9989 0.999 1.0005 0.9999 1.0011 u28 0.9897 0.9972 1.0022 1.0005 0.9981 0.999 0.9991 1.0005 0.9999 1.0011 u29 0.9899 0.9971 1.0023 1.0005 0.9981 0.9989 0.9991 1.0005 0.9999 1.0011 u30 0.99 0.9969 1.0023 1.0005 0.998 0.9989 0.9991 1.0005 0.9999 1.0011 u31 0.9899 0.997 1.0023 1.0005 0.998 0.9989 0.9991 1.0005 0.9999 1.001 u32 0.9905 0.9848 0.9969 1.001 1.0012 0.9984 0.9927 0.9937 0.998 1.0013 u33 0.9907 0.9847 0.997 1.001 1.0012 0.9984 0.9927 0.9937 0.998 1.0013 u34 0.9906 0.9849 0.9971 1.0009 1.0011 0.9983 0.9926 0.9937 0.998 1.0013 u35 0.9904 0.9849 0.9971 1.0009 1.0011 0.9983 0.9926 0.9937 0.998 1.0012 u36 0.9891 0.9851 0.9978 1.001 1.0011 0.9983 0.9925 0.9937 0.9979 1.0012 u37 0.9892 0.985 0.9979 1.001 1.0011 0.9983 0.9925 0.9937 0.9979 1.0012 u38 0.9895 0.9848 0.9979 1.001 1.001 0.9983 0.9925 0.9937 0.9979 1.0011 u39 0.9892 0.9849 0.9979 1.001 1.001 0.9983 0.9925 0.9937 0.9979 1.0011 u40 0.9844 0.9851 0.9989 1.0015 1.0009 0.9981 0.9921 0.9935 0.9978 1.0011 u41 0.9846 0.985 0.999 1.0015 1.0009 0.9981 0.9921 0.9935 0.9978 1.0011 u42 0.9847 0.9851 0.9991 1.0014 1.0009 0.9981 0.992 0.9935 0.9977 1.0011 u43 0.9847 0.9851 0.999 1.0014 1.0009 0.9981 0.992 0.9935 0.9977 1.0011 u44 0.9859 0.985 0.9984 1.0013 1.0009 0.9981 0.9921 0.9935 0.9978 1.0011 u45 0.9861 0.9849 0.9985 1.0013 1.0009 0.9981 0.9921 0.9935 0.9978 1.0011 u46 0.9862 0.9847 0.9984 1.0013 1.0009 0.9982 0.9921 0.9935 0.9978 1.0011 u47 0.9863 0.9847 0.9984 1.0013 1.001 0.9982 0.992 0.9935 0.9978 1.0011 u48 0.994 0.9872 0.9979 0.9999 1.0008 0.9988 0.9923 0.9933 0.9981 1.0012 u49 0.9941 0.9871 0.998 0.9999 1.0008 0.9988 0.9923 0.9933 0.9981 1.0012 u50 0.9941 0.9873 0.9981 0.9999 1.0008 0.9988 0.9923 0.9933 0.9981 1.0012 u51 0.994 0.9874 0.998 0.9999 1.0009 0.9988 0.9923 0.9933 0.9981 1.0012 u52 0.9929 0.9876 0.9987 1 1.0009 0.9988 0.9922 0.9934 0.9981 1.0013 u53 0.993 0.9875 0.9988 1 1.001 0.9988 0.9922 0.9934 0.9981 1.0013 u54 0.9932 0.9874 0.9987 1 1.0011 0.9988 0.9922 0.9934 0.9981 1.0013 u55 0.9932 0.9874 0.9987 1 1.0012 0.9989 0.9922 0.9934 0.9981 1.0014 u56 0.9967 0.9871 0.9979 0.9995 1.0013 0.9991 0.9926 0.9936 0.9983 1.0014 u57 0.9968 0.9871 0.9979 0.9994 1.0014 0.9992 0.9926 0.9936 0.9983 1.0014 u58 0.9968 0.9873 0.9979 0.9994 1.0015 0.9992 0.9925 0.9936 0.9983 1.0015 u59 0.9968 0.9873 0.9979 0.9994 1.0016 0.9992 0.9925 0.9937 0.9983 1.0015 u60 0.9979 0.9871 0.9973 0.9993 1.0017 0.9993 0.9926 0.9936 0.9983 1.0015 u61 0.9979 0.9871 0.9973 0.9993 1.0018 0.9993 0.9926 0.9936 0.9983 1.0016 u62 0.9982 0.987 0.9972 0.9993 1.0019 0.9994 0.9926 0.9936 0.9983 1.0017 u63 0.9981 0.987 0.9972 0.9993 1.0021 0.9994 0.9926 0.9936 0.9983 1.0017 u64 0.9982 0.9759 0.9698 0.9685 0.9806 1.0019 1.0454 1.1588 1.5058 2.3723 u65 0.9984 0.9759 0.97 0.9684 0.9806 1.002 1.0454 1.1588 1.5057 2.3723 u66 0.9985 0.9761 0.9702 0.9683 0.9807 1.0021 1.0454 1.1588 1.5057 2.3724 u67 0.9985 0.9762 0.9703 0.9682 0.9807 1.0022 1.0454 1.1588 1.5057 2.3724 u68 0.9976 0.9764 0.9711 0.9682 0.9807 1.0023 1.0453 1.1589 1.5057 2.3725 u69 0.9977 0.9764 0.9714 0.9681 0.9808 1.0024 1.0453 1.1589 1.5057 2.3725 u70 0.998 0.9762 0.9714 0.968 0.9808 1.0025 1.0453 1.1589 1.5057 2.3726 u71 0.9982 0.9762 0.9715 0.968 0.9808 1.0026 1.0453 1.1589 1.5057 2.3726 u72 0.9948 0.9766 0.9726 0.9683 0.9808 1.0025 1.0449 1.1586 1.5057 2.3725 u73 0.995 0.9765 0.9727 0.9682 0.9808 1.0026 1.0449 1.1586 1.5057 2.3726 u74 0.9951 0.9768 0.9728 0.9682 0.9808 1.0026 1.0448 1.1587 1.5057 2.3726 u75 0.9952 0.9768 0.9729 0.9681 0.9808 1.0027 1.0448 1.1587 1.5057 2.3726 u76 0.9963 0.9766 0.9723 0.968 0.9808 1.0028 1.0449 1.1587 1.5056 2.3726 u77 0.9965 0.9765 0.9724 0.9679 0.9808 1.0029 1.0449 1.1587 1.5056 2.3726 u78 0.9968 0.9764 0.9725 0.9679 0.9808 1.0029 1.0449 1.1587 1.5056 2.3726 u79 0.997 0.9765 0.9725 0.9679 0.9808 1.003 1.0449 1.1587 1.5055 2.3726 u80 0.9907 0.9741 0.9734 0.9688 0.9813 1.0024 1.0445 1.1587 1.5063 2.3732 u81 0.991 0.974 0.9735 0.9687 0.9813 1.0024 1.0445 1.1587 1.5063 2.3732 u82 0.991 0.9742 0.9736 0.9687 0.9813 1.0024 1.0444 1.1587 1.5063 2.3732 u83 0.9911 0.9743 0.9736 0.9687 0.9813 1.0025 1.0444 1.1587 1.5063 2.3731 u84 0.9902 0.9746 0.9743 0.9687 0.9813 1.0025 1.0443 1.1588 1.5063 2.3731 u85 0.9904 0.9745 0.9743 0.9687 0.9813 1.0025 1.0443 1.1588 1.5063 2.3731 u86 0.9907 0.9744 0.9743 0.9687 0.9813 1.0025 1.0443 1.1588 1.5063 2.3731 u87 0.9909 0.9744 0.9743 0.9687 0.9813 1.0025 1.0443 1.1588 1.5062 2.373 u88 0.9943 0.9742 0.9734 0.9682 0.9814 1.0027 1.0447 1.1592 1.5062 2.373 u89 0.9945 0.9742 0.9735 0.9682 0.9814 1.0027 1.0447 1.1592 1.5061 2.373 u90 0.9945 0.9744 0.9735 0.9682 0.9814 1.0027 1.0446 1.1592 1.5061 2.3729 u91 0.9947 0.9744 0.9734 0.9682 0.9814 1.0027 1.0446 1.1592 1.5061 2.3728 u92 0.9959 0.9743 0.9728 0.9681 0.9813 1.0028 1.0447 1.1592 1.506 2.3728 u93 0.996 0.9742 0.9729 0.9681 0.9813 1.0027 1.0447 1.1592 1.506 2.3727 u94 0.9964 0.9741 0.9728 0.9681 0.9813 1.0027 1.0447 1.1592 1.506 2.3726 u95 0.9965 0.9742 0.9727 0.9681 0.9813 1.0027 1.0446 1.1592 1.506 2.3725 u96 0.993 0.9848 0.9764 0.9687 0.9789 1.0046 1.0516 1.1657 1.5095 2.372 u97 0.9933 0.9847 0.9765 0.9687 0.9789 1.0046 1.0515 1.1657 1.5095 2.3719 u98 0.9935 0.985 0.9765 0.9687 0.9789 1.0046 1.0515 1.1657 1.5095 2.3718 u99 0.9936 0.9851 0.9765 0.9687 0.9789 1.0045 1.0515 1.1658 1.5094 2.3718 u100 0.9923 0.9853 0.9771 0.9688 0.9789 1.0044 1.0514 1.1658 1.5094 2.3717 u101 0.9927 0.9853 0.9771 0.9688 0.9789 1.0044 1.0513 1.1659 1.5094 2.3717 u102 0.993 0.9851 0.9771 0.9688 0.9789 1.0044 1.0514 1.1659 1.5094 2.3717 u103 0.993 0.9851 0.9771 0.9689 0.9789 1.0043 1.0513 1.1659 1.5094 2.3717 u104 0.9886 0.9855 0.9779 0.9693 0.9789 1.0041 1.0509 1.1657 1.5094 2.3716 u105 0.9888 0.9854 0.9779 0.9693 0.9788 1.004 1.0508 1.1657 1.5094 2.3716 u106 0.989 0.9856 0.978 0.9693 0.9788 1.0039 1.0508 1.1658 1.5093 2.3717 u107 0.9891 0.9857 0.9779 0.9693 0.9788 1.0039 1.0508 1.1658 1.5093 2.3717 u108 0.9905 0.9856 0.9773 0.9693 0.9788 1.0039 1.0508 1.1658 1.5093 2.3717 u109 0.9907 0.9855 0.9773 0.9693 0.9788 1.0038 1.0508 1.1658 1.5092 2.3718 u110 0.9911 0.9854 0.9773 0.9693 0.9788 1.0037 1.0508 1.1659 1.5092 2.3718 u111 0.9913 0.9854 0.9772 0.9694 0.9787 1.0037 1.0507 1.1659 1.5092 2.3719 u112 0.9986 0.9879 0.9766 0.9684 0.9783 1.0042 1.0511 1.166 1.5084 2.3713 u113 0.999 0.9878 0.9766 0.9684 0.9783 1.0042 1.0511 1.166 1.5083 2.3713 u114 0.9991 0.9881 0.9767 0.9684 0.9783 1.0041 1.051 1.166 1.5083 2.3714 u115 0.9993 0.9882 0.9766 0.9685 0.9783 1.004 1.051 1.1661 1.5083 2.3714 u116 0.9982 0.9884 0.9773 0.9686 0.9783 1.0039 1.0509 1.1662 1.5083 2.3715 u117 0.9985 0.9884 0.9773 0.9686 0.9783 1.0038 1.0508 1.1662 1.5083 2.3715 u118 0.9989 0.9883 0.9773 0.9686 0.9783 1.0038 1.0508 1.1662 1.5082 2.3716 u119 0.9991 0.9884 0.9773 0.9687 0.9783 1.0037 1.0508 1.1663 1.5082 2.3717 u120 1.0043 0.9882 0.9765 0.9683 0.9783 1.0038 1.0512 1.1666 1.5081 2.3718 u121 1.0047 0.9882 0.9765 0.9683 0.9783 1.0038 1.0511 1.1667 1.5081 2.3719 u122 1.0049 0.9884 0.9766 0.9683 0.9783 1.0037 1.0511 1.1667 1.5081 2.3719 u123 1.005 0.9885 0.9765 0.9684 0.9783 1.0036 1.051 1.1667 1.508 2.3721 u124 1.0066 0.9884 0.9759 0.9683 0.9782 1.0036 1.0511 1.1667 1.508 2.3721 u125 1.007 0.9884 0.976 0.9683 0.9782 1.0035 1.051 1.1668 1.5079 2.3722 u126 1.0073 0.9882 0.976 0.9683 0.9782 1.0035 1.051 1.1668 1.5079 2.3723 u127 1.0077 0.9883 0.976 0.9684 0.9782 1.0034 1.0509 1.1668 1.5079 2.3724 u128 1.8229 2.2059 2.557 2.7668 2.8933 2.9656 3.0137 3.104 3.4603 4.4018 u129 1.8236 2.2057 2.5572 2.7668 2.8933 2.9656 3.0136 3.104 3.4604 4.4018 u130 1.8237 2.2057 2.5575 2.7668 2.8932 2.9657 3.0136 3.1039 3.4604 4.4018 u131 1.823 2.206 2.5573 2.7668 2.8932 2.9657 3.0135 3.1038 3.4604 4.4018 u132 1.8197 2.2051 2.5583 2.7673 2.8932 2.9658 3.0135 3.1036 3.4604 4.4018 u133 1.8204 2.2049 2.5585 2.7673 2.8932 2.9658 3.0135 3.1036 3.4605 4.4019 u134 1.8205 2.205 2.5583 2.7673 2.8933 2.9658 3.0134 3.1035 3.4605 4.4019 u135 1.8198 2.2052 2.5582 2.7674 2.8933 2.9659 3.0133 3.1035 3.4606 4.4019 u136 1.809 2.2018 2.5583 2.7687 2.8931 2.965 3.0139 3.1038 3.4605 4.4018 u137 1.8097 2.2016 2.5585 2.7687 2.8931 2.965 3.0138 3.1037 3.4605 4.4018 u138 1.8097 2.2016 2.5588 2.7687 2.893 2.9651 3.0138 3.1037 3.4606 4.4019 u139 1.809 2.2019 2.5586 2.7687 2.893 2.9651 3.0138 3.1036 3.4606 4.4019 u140 1.8123 2.2027 2.5577 2.7683 2.893 2.9652 3.0136 3.1036 3.4607 4.4019 u141 1.813 2.2025 2.5579 2.7683 2.893 2.9652 3.0136 3.1036 3.4607 4.4019 u142 1.8131 2.2026 2.5578 2.7683 2.8931 2.9652 3.0135 3.1036 3.4608 4.402 u143 1.8124 2.2029 2.5576 2.7684 2.8931 2.9653 3.0134 3.1035 3.4608 4.402 u144 1.7982 2.1934 2.5569 2.7698 2.8937 2.9645 3.0103 3.1014 3.4598 4.4024 u145 1.7989 2.1932 2.5571 2.7698 2.8937 2.9646 3.0103 3.1013 3.4598 4.4025 u146 1.7989 2.1932 2.5574 2.7698 2.8936 2.9646 3.0103 3.1013 3.4598 4.4025 u147 1.7982 2.1935 2.5572 2.7698 2.8936 2.9646 3.0103 3.1012 3.4599 4.4025 u148 1.795 2.1927 2.5582 2.7703 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42.1031 44.34 44.641 45.2965 47.1836 49.9228 82.6662 87.29 u328 24.0229 26.4321 42.13 44.5399 45.6123 46.8504 48.8059 51.5793 85.2449 90.0056 u329 24.0234 26.4321 42.1296 44.5403 45.6119 46.8494 48.806 51.5795 85.2464 90.0061 u330 24.0235 26.4319 42.1314 44.5407 45.6125 46.8499 48.8062 51.5803 85.2464 90.0043 u331 24.0237 26.4317 42.1313 44.5403 45.6125 46.8498 48.8063 51.5798 85.2455 90.006 u332 24.0237 26.432 42.1299 44.5402 45.6123 46.8496 48.8058 51.5802 85.2453 89.9439 u333 24.0233 26.4323 42.1299 44.5408 45.6119 46.8494 48.8058 51.5804 85.2461 89.942 u334 24.0234 26.4325 42.1286 44.5405 45.6112 46.8495 48.8058 51.5795 85.2459 89.9415 u335 24.0234 26.4325 42.129 44.5401 45.6115 46.8502 48.8059 51.5791 85.2451 89.9442 u336 25.68 28.1834 44.7117 46.9632 47.5309 48.5352 50.4855 53.2791 87.8824 92.7763 u337 25.6799 28.1835 44.7098 46.9631 47.5304 48.5363 50.4853 53.2802 87.883 92.7802 u338 25.6799 28.1833 44.706 46.9621 47.5299 48.5357 50.485 53.2792 87.8796 92.7806 u339 25.68 28.1832 44.7081 46.9625 47.5304 48.5363 50.486 53.2783 87.8793 92.7779 u340 25.6799 28.1826 44.7051 46.9613 47.5293 48.5357 50.4861 53.2784 87.8789 92.6155 u341 25.68 28.1827 44.7028 46.961 47.5298 48.5357 50.4857 53.2786 87.8799 92.6195 u342 25.6801 28.1829 44.7067 46.9621 47.5281 48.5365 50.4863 53.28 87.8832 92.6178 u343 25.6803 28.1828 44.7086 46.9623 47.5299 48.5355 50.4856 53.2797 87.8821 92.6163 u344 25.6829 28.2004 44.8014 47.4648 48.9479 50.1963 52.1866 55.0115 90.5612 95.6812 u345 25.683 28.2005 44.7984 47.465 48.9484 50.1955 52.1865 55.0116 90.561 95.6836 u346 25.6831 28.2003 44.794 47.4647 48.9484 50.1955 52.1867 55.0126 90.5727 95.6776 u347 25.6832 28.2003 44.7968 47.4647 48.9481 50.1957 52.1866 55.0123 90.5734 95.6757 u348 25.6832 28.2011 44.7986 47.465 48.9474 50.1956 52.1866 55.0122 90.5719 95.3043 u349 25.6832 28.2011 44.7958 47.4649 48.9484 50.1951 52.1865 55.0124 90.5726 95.3 u350 25.6832 28.2013 44.8011 47.4652 48.9479 50.1952 52.1866 55.0112 90.5596 95.3008 u351 25.6833 28.2013 44.8045 47.4653 48.9474 50.1963 52.1869 55.011 90.5593 95.3053 u352 27.4324 30.0079 47.3803 49.7275 50.7917 51.9472 53.9414 56.7898 93.3305 98.7881 u353 27.4326 30.0079 47.3822 49.7275 50.7913 51.9464 53.9419 56.7898 93.33 98.7872 u354 27.4326 30.008 47.3861 49.7276 50.7912 51.9466 53.9427 56.7898 93.2881 98.7921 u355 27.4325 30.008 47.3848 49.7279 50.7911 51.9464 53.9423 56.7896 93.2892 98.7926 u356 27.4322 30.0081 47.3856 49.7276 50.7911 51.9465 53.9425 56.7864 93.2888 98.0402 u357 27.4323 30.0082 47.3874 49.7276 50.7921 51.9457 53.9431 56.7864 93.2888 98.0416 u358 27.4324 30.0081 47.3833 49.728 50.7916 51.9457 53.9422 56.7862 93.3305 98.039 u359 27.4326 30.0081 47.3812 49.7283 50.7916 51.947 53.9419 56.7864 93.3312 98.0396 u360 27.4467 30.0742 47.6581 50.7504 52.4786 53.7089 55.7333 58.6094 96.0561 102.1968 u361 27.447 30.0741 47.6603 50.7506 52.4787 53.7087 55.733 58.6091 96.0551 102.1942 u362 27.4474 30.0742 47.6693 50.7503 52.4777 53.7096 55.7321 58.6086 96.1752 102.1967 u363 27.4475 30.0742 47.6663 50.7503 52.4775 53.7095 55.7323 58.6088 96.1761 102.1985 u364 27.4477 30.0744 47.6625 50.7501 52.4776 53.7092 55.733 58.5968 96.1765 100.9724 u365 27.4476 30.0744 47.6649 50.7502 52.4773 53.7089 55.733 58.5962 96.1755 100.97 u366 27.4476 30.0743 47.6558 50.7506 52.4783 53.708 55.7339 58.5967 96.0552 100.9707 u367 27.4475 30.0743 47.6537 50.7506 52.4785 53.7078 55.7339 58.5973 96.0554 100.9662 u368 29.2514 31.8831 50.1401 52.862 54.3503 55.5476 57.5757 60.4822 99.1599 105.8048 u369 29.2514 31.8831 50.1394 52.8603 54.3509 55.5483 57.5761 60.4825 99.1588 105.808 u370 29.2517 31.8835 50.1327 52.8575 54.3518 55.547 57.5761 60.4819 98.8465 105.8083 u371 29.2514 31.8836 50.1344 52.8591 54.3514 55.5465 57.5762 60.4819 98.8466 105.8062 u372 29.2513 31.8843 50.1314 52.862 54.3514 55.5468 57.5795 60.4458 98.8455 104.2296 u373 29.2515 31.8842 50.1295 52.8596 54.3515 55.5464 57.5795 60.4455 98.8471 104.2253 u374 29.2512 31.8838 50.1378 52.8616 54.3507 55.5473 57.579 60.4465 99.1586 104.2289 u375 29.2512 31.8837 50.1408 52.8554 54.3502 55.5472 57.5795 60.4466 99.1592 104.2252 u376 29.3146 32.0919 50.8367 54.4305 56.2047 57.4235 59.4649 62.4228 101.6819 109.5439 u377 29.3148 32.092 50.8358 54.4305 56.2041 57.4231 59.4657 62.4236 101.6812 109.5443 u378 29.3152 32.092 50.829 54.4309 56.2044 57.4238 59.4666 62.4241 102.3729 109.5424 u379 29.315 32.092 50.8299 54.4308 56.2043 57.4237 59.4651 62.4233 102.3738 109.5437 u380 29.3148 32.0916 50.8332 54.4314 56.204 57.4234 59.4763 62.3241 102.372 107.7734 u381 29.3149 32.0917 50.8321 54.4319 56.2039 57.423 59.4772 62.3237 102.372 107.7724 u382 29.3146 32.0917 50.837 54.4314 56.2037 57.4222 59.4778 62.324 101.6835 107.772 u383 29.3145 32.0916 50.8364 54.4314 56.204 57.4217 59.4773 62.3232 101.6817 107.7719 u384 31.1422 33.8296 53.1439 56.4692 58.1685 59.3709 61.4077 64.4733 105.9256 113.4139 u385 31.1424 33.8295 53.1513 56.47 58.169 59.3699 61.4071 64.473 105.9245 113.4138 u386 31.1432 33.8295 53.1503 56.4696 58.1697 59.37 61.4067 64.4735 104.7031 113.4124 u387 31.1432 33.8297 53.1495 56.4694 58.1695 59.3697 61.4081 64.4732 104.7025 113.4128 u388 31.143 33.8295 53.1525 56.4686 58.1696 59.3727 61.4431 64.2245 104.7024 111.5199 u389 31.1432 33.8294 53.1544 56.4694 58.1689 59.3717 61.4421 64.2237 104.7038 111.5204 u390 31.1425 33.8293 53.1519 56.468 58.1702 59.3723 61.4424 64.2236 105.9264 111.5221 u391 31.1422 33.8293 53.1478 56.4685 58.1685 59.3726 61.4433 64.224 105.9274 111.5227 u392 31.3543 34.3575 54.4905 58.3807 60.1766 61.3716 63.3843 66.7059 108.0895 117.4159 u393 31.3546 34.3574 54.4909 58.3805 60.1767 61.3716 63.3855 66.7049 108.09 117.4172 u394 31.3542 34.3577 54.4916 58.3801 60.1757 61.3716 63.3862 66.7046 109.7497 117.4167 u395 31.3543 34.3577 54.4917 58.3803 60.1752 61.3717 63.3852 66.7054 109.75 117.4155 u396 31.3543 34.3569 54.488 58.3806 60.1757 61.3836 63.4874 66.1683 109.7512 115.4305 u397 31.3542 34.3569 54.4898 58.3807 60.1761 61.3837 63.4885 66.1685 109.75 115.4324 u398 31.3549 34.3566 54.4884 58.3813 60.1769 61.3836 63.4883 66.1684 108.0909 115.4313 u399 31.3549 34.3567 54.4884 58.3812 60.1765 61.3838 63.4869 66.1695 108.0903 115.4307 u400 33.1169 35.9896 56.6879 60.487 62.2779 63.4405 65.3937 69.185 113.739 121.5803 u401 33.1169 35.9896 56.6844 60.487 62.2778 63.4406 65.3938 69.1858 113.738 121.5818 u402 33.117 35.9894 56.6852 60.4881 62.2784 63.4406 65.3932 69.1843 111.838 121.5806 u403 33.1171 35.9896 56.679 60.4856 62.2789 63.4402 65.3927 69.1843 111.8366 121.5801 u404 33.1162 35.9902 56.6834 60.4868 62.2824 63.4829 65.6593 68.2735 111.8392 119.501 u405 33.1162 35.99 56.6844 60.4873 62.2828 63.4832 65.6591 68.2725 111.8389 119.4989 u406 33.1162 35.9901 56.683 60.4855 62.2808 63.4832 65.6602 68.2743 113.7388 119.4963 u407 33.1163 35.9902 56.6857 60.4869 62.2817 63.4828 65.6609 68.272 113.7398 119.4989 u408 33.6746 37.0043 58.5751 62.6228 64.4478 65.5581 67.4583 71.848 115.8502 125.9235 u409 33.6747 37.0041 58.5786 62.6229 64.4474 65.5585 67.4579 71.8473 115.8494 125.9263 u410 33.6747 37.0045 58.578 62.6251 64.446 65.5593 67.4567 71.8498 117.9038 125.926 u411 33.6746 37.0046 58.5732 62.625 64.4462 65.5591 67.457 71.849 117.905 125.9239 u412 33.6744 37.0043 58.5769 62.6254 64.4653 65.6857 68.047 70.6516 117.906 123.7404 u413 33.6745 37.0043 58.5817 62.6256 64.465 65.6859 68.0463 70.6513 117.9053 123.7373 u414 33.6746 37.004 58.5823 62.6235 64.4662 65.6852 68.0463 70.6511 115.8503 123.7375 u415 33.6746 37.0041 58.5794 62.6237 64.4667 65.6848 68.0469 70.6513 115.8494 123.7391 u416 35.3469 38.5667 60.7984 64.8988 66.6968 67.7178 69.7144 74.6428 122.2731 130.4834 u417 35.3462 38.5671 60.7938 64.8982 66.697 67.7181 69.7169 74.6445 122.2717 130.4845 u418 35.3463 38.5668 60.7928 64.8888 66.6996 67.7156 69.7145 74.6426 120.0848 130.4848 u419 35.3454 38.5661 60.7991 64.8897 66.6985 67.7162 69.7153 74.6434 120.0863 130.4845 u420 35.3462 38.5665 60.8037 64.8875 66.7683 68.0546 70.7304 73.2875 120.0867 128.1823 u421 35.3464 38.5663 60.7976 64.888 66.7688 68.0536 70.7303 73.286 120.0872 128.1835 u422 35.3462 38.5662 60.7978 64.8966 66.767 68.055 70.7312 73.2862 122.2726 128.1856 u423 35.346 38.5664 60.8033 64.8958 66.7664 68.0545 70.7309 73.2865 122.2712 128.1841 u424 36.439 39.9819 63.0245 67.2409 69.0131 69.9624 72.3007 77.5818 124.5566 135.2748 u425 36.4389 39.9819 63.0334 67.2411 69.0116 69.9624 72.2992 77.5821 124.555 135.2748 u426 36.4388 39.9816 63.0291 67.2821 69.0111 69.9648 72.2987 77.5812 126.8755 135.2699 u427 36.4388 39.9816 63.0224 67.2818 69.0121 69.9632 72.2995 77.5812 126.8755 135.274 u428 36.4372 39.981 63.0324 67.2796 69.2216 70.7043 73.6294 76.1158 126.8764 132.8516 u429 36.4371 39.9811 63.0391 67.28 69.2209 70.7049 73.6296 76.1172 126.8743 132.8499 u430 36.4373 39.9814 63.0434 67.2391 69.2229 70.7039 73.6298 76.1163 124.5551 132.8517 u431 36.4373 39.9814 63.0395 67.2389 69.224 70.7038 73.63 76.1155 124.5549 132.8517 u432 38.0581 41.597 65.4426 69.8384 71.3939 72.484 75.1851 80.6954 131.7401 140.3531 u433 38.0581 41.597 65.437 69.8374 71.3937 72.4836 75.1856 80.6941 131.7374 140.3414 u434 38.0584 41.5966 65.4323 69.6926 71.3933 72.4838 75.1867 80.6941 129.2792 140.2923 u435 38.0579 41.5969 65.4366 69.6932 71.3933 72.4835 75.1849 80.6942 129.2761 140.3061 u436 38.0587 41.6018 65.4716 69.6925 71.9276 73.7073 76.6942 79.1261 129.2748 137.7683 u437 38.0592 41.602 65.4633 69.6916 71.9287 73.7087 76.6948 79.1257 129.2769 137.7728 u438 38.0599 41.6019 65.4693 69.8358 71.9266 73.7081 76.6942 79.1243 131.7393 137.7598 u439 38.0603 41.602 65.4688 69.8366 71.927 73.7071 76.6931 79.1254 131.7422 137.7543 u440 39.5865 43.2635 67.9368 72.2211 73.9634 75.4065 78.3141 84.0138 134.2818 145.8535 u441 39.5862 43.2637 67.9325 72.2209 73.9613 75.4072 78.3138 84.0103 134.2834 145.8523 u442 39.5857 43.2641 67.9324 72.6444 73.964 75.4072 78.3142 84.0092 136.9324 145.51 u443 39.5859 43.2639 67.9367 72.6426 73.9632 75.4057 78.3141 84.0136 136.9341 145.5114 u444 39.5926 43.2944 68.0571 72.6424 75.039 76.9509 79.9576 82.3296 136.8983 143.0163 u445 39.5924 43.2947 68.06 72.6439 75.0384 76.95 79.9569 82.3305 136.8987 143.0225 u446 39.5929 43.2944 68.0565 72.2221 75.0368 76.9504 79.9555 82.3309 134.2936 142.8933 u447 39.5931 43.2943 68.058 72.2221 75.037 76.9514 79.9567 82.3296 134.2932 142.8843 u448 41.3049 45.0367 70.55 75.8785 76.956 78.6861 81.6807 87.583 142.3095 152.3927 u449 41.3044 45.0369 70.551 75.8777 76.9562 78.6869 81.6788 87.5412 142.3095 152.3929 u450 41.3059 45.0372 70.5533 74.9068 76.9566 78.6864 81.6802 87.54 139.6908 151.1156 u451 41.3041 45.037 70.5437 74.9083 76.9558 78.6849 81.682 87.5826 139.6909 151.1177 u452 41.3431 45.1593 70.9454 74.909 78.5367 80.4284 83.4564 85.7515 139.5833 148.9446 u453 41.3437 45.1593 70.9451 74.9082 78.537 80.4263 83.4571 85.7633 139.5827 148.9429 u454 41.3425 45.1595 70.9502 75.8764 78.5358 80.4248 83.462 85.7636 142.6066 148.1995 u455 41.3421 45.1591 70.9507 75.8762 78.536 80.426 83.4608 85.7523 142.6046 148.2025 u456 43.095 46.8876 73.3354 78.0149 80.4441 82.2822 85.3085 91.5777 145.0999 160.0248 u457 43.0951 46.8875 73.3271 78.0151 80.4443 82.2819 85.3085 91.2426 145.1001 160.026 u458 43.0955 46.8877 73.3274 79.6456 80.4424 82.2793 85.3287 91.245 149.3668 158.0959 u459 43.0946 46.8877 73.3326 79.6467 80.4434 82.2787 85.3306 91.5801 149.3659 158.0948 u460 43.2624 47.2688 74.3079 79.6448 82.3285 84.2071 87.2159 89.3732 148.1043 156.1076 u461 43.2629 47.2693 74.3113 79.6449 82.3288 84.2076 87.2177 89.5043 148.1059 156.1043 u462 43.2609 47.2696 74.308 78.0177 82.3271 84.1959 87.2948 89.5041 145.7857 154.4256 u463 43.2602 47.2693 74.3189 78.0174 82.3277 84.1953 87.2925 89.3735 145.7856 154.4249 u464 45.0026 48.9244 76.577 83.8073 84.3678 86.249 89.1774 96.5297 155.4054 164.1738 u465 45.0038 48.9255 76.5782 83.8018 84.3672 86.2497 89.1764 95.4314 155.4023 164.1668 u466 45.0023 48.9249 76.5807 81.7443 84.3617 86.2023 89.3957 95.4302 153.2874 166.3172 u467 45.0034 48.9244 76.5796 81.7434 84.3632 86.2014 89.3987 96.5295 153.2858 166.3116 u468 45.4985 49.7981 78.3198 81.7438 86.5044 88.4294 91.1936 93.2095 151.536 168.5033 u469 45.4984 49.798 78.3199 81.7436 86.5033 88.4291 91.1957 93.9086 151.5386 168.4994 u470 45.4972 49.7981 78.3273 83.8017 86.4712 88.2699 91.7357 93.9109 157.4443 162.0943 u471 45.4976 49.7981 78.3238 83.8072 86.4722 88.2701 91.7341 93.2111 157.4372 162.0979 u472 47.1812 51.4008 80.5853 86.052 88.8102 90.8379 93.4148 102.3437 159.6629 178.0281 u473 47.1793 51.3999 80.5784 86.0775 88.8085 90.8395 93.4126 100.8371 159.7353 178.0888 u474 47.1792 51.3996 80.5778 88.3989 88.6874 90.4077 94.418 100.8385 161.4906 170.7864 u475 47.1775 51.3998 80.5826 88.5045 88.6874 90.407 94.4168 102.3437 162.0578 170.7885 u476 48.2602 52.8027 82.8266 88.5079 91.351 93.6197 96.0017 97.9904 164.329 173.1246 u477 48.2589 52.8033 82.8247 88.399 91.3517 93.6216 96.001 99.3405 166.9644 173.1339 u478 48.2571 52.8089 82.8635 86.0761 90.9752 92.7009 97.3717 99.3403 166.8286 175.5452 u479 48.2578 52.8079 82.8658 86.0498 90.9768 92.7021 97.3718 97.9893 164.9195 175.5667 u480 49.9204 54.4608 85.2749 94.3572 94.308 96.7916 98.9623 109.0638 171.9601 183.1706 u481 49.9207 54.4594 85.2789 93.4722 94.305 96.7938 98.9639 107.3125 169.4261 183.561 u482 49.9267 54.4959 85.4091 91.2062 93.4157 95.3759 100.5473 107.2919 169.3906 185.8604 u483 49.9295 54.4958 85.4157 90.8593 93.4156 95.3754 100.5491 109.138 172.0146 186.6658 u484 51.5221 56.1812 87.8379 90.8599 97.7921 100.2475 102.245 103.9362 174.6048 188.8092 u485 51.5246 56.181 87.8408 91.2098 97.7919 100.2473 102.2485 105.5795 177.7215 190.1516 u486 51.5879 56.3367 88.2852 93.4714 96.2548 98.5286 104.0024 105.5764 177.2994 180.5749 u487 51.5863 56.337 88.2862 94.3565 96.2546 98.5303 104.0187 103.9358 174.7609 180.7371 u488 53.3161 58.0275 90.6272 96.5321 106.0663 104.0424 105.8492 117.3113 183.2688 207.205 u489 53.3156 58.0272 90.6288 98.1431 105.9258 104.0839 105.9014 115.8266 181.0581 201.9648 u490 53.5603 58.5022 91.7549 100.2597 99.7346 102.1054 107.7543 114.8657 180.109 192.1819 u491 53.5598 58.5013 91.7452 102.7452 99.7353 102.1144 107.9239 118.618 184.8946 193.9278 u492 55.2561 60.1408 94.0274 102.094 101.6902 108.1702 109.7293 110.8906 187.0507 195.9463 u493 55.2536 60.1401 94.0225 100.3662 101.6823 108.5941 110.1842 113.2987 189.0814 197.9263 u494 55.9575 61.1933 95.9591 98.1398 103.7922 106.0702 111.8828 112.7799 191.2342 200.1039 u495 55.9545 61.193 95.9578 96.5259 103.7559 106.2142 112.8128 111.1046 193.4234 205.0979 u496 57.6385 62.8176 98.2729 110.7233 111.6839 113.1487 114.4232 130.5814 195.7412 217.4963 u497 57.642 62.8281 98.3185 112.2847 110.6768 114.6195 115.7969 132.6632 198.1371 214.7692 u498 59.0042 64.3876 100.6974 107.626 115.2945 110.4487 117.4144 126.718 200.6614 223.3043 u499 59.0342 64.465 100.9143 108.7795 113.6476 111.3842 119.0583 128.5997 203.2991 220.3407 u500 60.7329 66.1457 103.2898 104.8265 119.3173 120.0971 120.8309 120.1201 206.0702 229.6263 u501 60.8673 66.4305 103.9738 105.8718 117.3087 130.1909 127.7652 124.9348 208.9752 226.3983 u502 62.5426 68.0764 106.2703 114.3264 108.6353 116.3941 129.9928 123.2466 212.0266 212.1517 u503 63.0233 68.845 107.8059 116.3532 108.2046 118.2137 122.6547 121.632 215.2249 209.6442 u504 64.7063 70.4884 110.0966 118.6444 130.9001 122.984 134.8738 137.7682 218.5842 236.4769 u505 65.8405 71.9292 112.3906 121.1165 122.8929 125.2188 132.3583 135.4531 222.1134 244.6645 u506 67.5824 73.7057 115.0313 123.8409 125.3324 127.6202 125.6912 140.7453 225.8235 240.8179 u507 69.4139 75.665 117.9552 126.8307 128.0094 133.5832 137.548 143.3382 229.737 232.9769 u508 71.5481 77.8744 121.1796 130.1067 134.716 136.5634 140.4019 146.0965 233.8787 249.6594 u509 73.9871 80.3612 124.7913 133.7124 138.147 139.7863 143.479 149.0639 238.2892 253.9707 u510 76.7941 83.1813 128.8735 137.7296 141.9513 143.3296 146.8374 152.2948 243.1015 264.3589 u511 80.1201 86.4858 133.6086 142.366 146.2886 147.35 150.6362 155.922 248.5007 259.1528

Obviously, numerous modifications and variations of the present disclosure are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the disclosure may be practiced otherwise than as specifically described herein (e.g., if the NUC position vectors are rounded to a smaller number of digits).

In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

In so far as embodiments of the disclosure have been described as being implemented, at least in part, by software-controlled data processing apparatus, it will be appreciated that a non-transitory machine-readable medium carrying such software, such as an optical disk, a magnetic disk, semiconductor memory or the like, is also considered to represent an embodiment of the present disclosure. Further, such a software may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.

A circuit that may be used for implementing one or more of the elements of the claimed apparatus is a structural assemblage of electronic components including conventional circuit elements, integrated circuits including application specific integrated circuits, standard integrated circuits, application specific standard products, and field programmable gate arrays. Further a circuit includes central processing units, graphics processing units, and microprocessors which are programmed or configured according to software code. A circuit does not include pure software, although a circuit includes the above-described hardware executing software.

Any reference signs in the claims should not be construed as limiting the scope. 

1. A coding and modulation apparatus, comprising: an encoder configured to encode input data into cell words; a modulator configured to modulate the cell words into constellation values of a non-uniform constellation; and a converter that converts the constellation values into one or more data streams, wherein the non-uniform constellation is a 1024-QAM constellation, the modulator is configured to use, based on a total number M constellation points of the non-uniform constellation, the non-uniform constellation defined by a constellation position vector u_(1 . . . v), wherein v=(sqrt(M)/2)−1: u₁ 1.0003 u₂ 1.0149 u₃ 1.0158 u₄ 2.6848 u₅ 2.6903 u₆ 2.882 u₇ 2.8747 u₈ 4.7815 u₉ 4.7619 u₁₀ 5.5779 u₁₁ 5.6434 u₁₂ 7.3854 u₁₃ 7.8797 u₁₄ 9.635 u₁₅ 11.7874,

M=1024, and each constellation position of the constellation position vector describes five bit labels for both of real and imaginary components of the non-uniform constellation according to the following: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉ −u₈ −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1  u₁  u₂  u₃  u₄  u₅  u₆  u₇  u₈  u₉  u₁₀  u₁₁  u₁₂  u₁₃  u₁₄ u₁₅


2. The coding and modulation apparatus according to claim 1, wherein the non-uniform constellation further includes a constellation position u₀ with a value of
 1. 3. The coding and modulation apparatus according to claim 2, wherein the positions u₀ . . . u₁₅ define cell words representing binary input data in a constellation.
 4. The coding and modulation apparatus according to claim 3, wherein each position of u₀ . . . u₁₅ represents respectively a positive and negative real and imaginary value which, when plotted against each other on a real and imaginary axis, represent positions of 1024 bit labels, the bit labels corresponding to the cell words.
 5. The coding and modulation apparatus according to claim 4, wherein each cell word comprises 10 bits.
 6. The coding and modulation apparatus according to claim 4, wherein a bit label corresponding to one constellation position on the real and imaginary axis differs by only one bit from a bit label for an adjacent constellation position.
 7. The coding and modulation apparatus according to claim 1, wherein the encoder is a forward error correction code encoder.
 8. The coding and modulation apparatus according to claim 2, wherein the modulator is configured to use the non-uniform constellation so that, when power is normalized, the non-uniform constellation is represented by a constellation position vector u_(0 . . . v): u₀ 0.1275 u₁ 0.1276 u₂ 0.1294 u₃ 0.1295 u₄ 0.3424 u₅ 0.3431 u₆ 0.3675 u₇ 0.3666 u₈ 0.6097 u₉ 0.6072 u₁₀ 0.7113 u₁₁ 0.7196 u₁₂ 0.9418 u₁₃ 1.0048 u₁₄ 1.2286 u₁₅ 1.5031.


9. The coding and modulation apparatus as claimed in claim 8, wherein each position of u₀ . . . u₁₅ represents respectively a positive and negative real and imaginary value which, when plotted against each other on a real and imaginary axis, represent positions of 1024 bit labels, the bit labels corresponding to the cell words.
 10. A transmission apparatus, comprising: the coding and modulation apparatus as recited in claim 1; and a transmitter configured to transmit the one or more data streams.
 11. The transmission apparatus of claim 10, wherein the transmitter is configured to transmit the one or more data streams for terrestrial delivery having fading channels.
 12. A communications system, comprising: one or more of the transmission apparatus as claimed in claim 10; and one or more receiving apparatus.
 13. A coding and modulation method, comprising: encoding input data into cell words; modulating, by circuitry, the cell words into constellation values of a non-uniform constellation; and converting said constellation values into one or more data streams, wherein the non-uniform constellation is a 1024-QAM constellation, in the modulating, the circuitry uses, based on a total number M constellation points of the non-uniform constellation, the non-uniform constellation defined by a constellation position vector u_(1 . . . v), wherein v=(sqrt(M)/2)−1: u₁ 1.0003 u₂ 1.0149 u₃ 1.0158 u₄ 2.6848 u₅ 2.6903 u₆ 2.882 u₇ 2.8747 u₈ 4.7815 u₉ 4.7619 u₁₀ 5.5779 u₁₁ 5.6434 u₁₂ 7.3854 u₁₃ 7.8797 u₁₄ 9.635 u₁₅ 11.7874, and

M=1024, and each constellation position of the constellation position vector describes five bit labels for both of real and imaginary components of the non-uniform constellation according to the following: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉ −u₈ −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1  u₁  u₂  u₃  u₄  u₅  u₆  u₇  u₈  u₉  u₁₀  u₁₁  u₁₂  u₁₃  u₁₄ u₁₅


14. The coding and modulation method according to claim 13, further comprising modifying the non-uniform constellation to further include a constellation position u₀ with a value of
 1. 15. The coding and modulation method according to claim 14, wherein in the modulating, the circuitry uses the non-uniform constellation so that, when power is normalized, the non-uniform constellation is represented by a constellation position vector u_(0 . . . v): u₀ 0.1275 u₁ 0.1276 u₂ 0.1294 u₃ 0.1295 u₄ 0.3424 u₅ 0.3431 u₆ 0.3675 u₇ 0.3666 u₈ 0.6097 u9 0.6072 u₁₀ 0.7113 u₁₁ 0.7196 u₁₂ 0.9418 u₁₃ 1.0048 u₁₄ 1.2286 u₁₅ 1.5031.


16. A non-transitory computer readable medium including computer program instructions which, when executed by a computer including the circuitry, causes the computer to perform the coding and modulation method of claim
 13. 17. A receiving method, comprising: demodulating cell words modulated and encoded according to the coding and modulation method of claim
 13. 18. A decoder and demodulation apparatus, comprising: a converted that converts one or more data streams into constellation values of a non-uniform constellation; a demodulator configured to demodulate the constellation values into cell words; and a decoder configured to decode cell words into input data, wherein the non-uniform constellation is a 1024-QAM constellation, the demodulator is configured to use, based on a total number M constellation points of the non-uniform constellation, the non-uniform constellation is defined by a constellation position vector u_(1 . . . v), v=(sqrt(M)/2)−1: u₁ 1.0003 u₂ 1.0149 u₃ 1.0158 u₄ 2.6848 u₅ 2.6903 u₆ 2.882 u₇ 2.8747 u₈ 4.7815 u₉ 4.7619 u₁₀ 5.5779 u₁₁ 5.6434 u₁₂ 7.3854 u₁₃ 7.8797 u₁₄ 9.635 u₁₅ 11.7874,

M=1024, and each constellation position of the constellation position vector describes five bit labels for both of real and imaginary components of the non-uniform constellation according to the following: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉ −u₈ −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1  u₁  u₂  u₃  u₄  u₅  u₆  u₇  u₈  u₉  u₁₀  u₁₁  u₁₂  u₁₃  u₁₄ u₁₅


19. The decoder and demodulation apparatus according to claim 18, wherein the non-uniform constellation further includes a constellation position u₀ with a value of 1, and the demodulator is configured to use the non-uniform constellation so that, when power is normalized, the non-uniform constellation is represented by a constellation position vector u_(0 . . . v): u₀ 0.1275 u₁ 0.1276 u₂ 0.1294 u₃ 0.1295 u₄ 0.3424 u₅ 0.3431 u₆ 0.3675 u₇ 0.3666 u₈ 0.6097 u9 0.6072 u₁₀ 0.7113 u₁₁ 0.7196 u₁₂ 0.9418 u₁₃ 1.0048 u₁₄ 1.2286 u₁₅ 1.5031.


20. The receiver apparatus according to claim 19, wherein each position of u₀ . . . u₁₅ represents respectively a positive and negative real and imaginary value which, when plotted against each other on a real and imaginary axis, represent positions of 1024 bit labels, the bit labels corresponding to the cell words.
 21. A receiver apparatus, comprising: the decoder and demodulation apparatus according to claim 18; and a receiver configured to receive the one or more data streams.
 22. The receiver apparatus according to claim 21, wherein the receiver is configured to receive the one or more data streams for terrestrial delivery having fading channels. 